Supramolecular Synthon Frustration Leads to Crystal Structures with Z

Multiple Molecules in the Asymmetric Unit (Z′ > 1) and the Formation of False Conglomerate Crystal Structures. Roger Bishop and Marcia L. Scudder...
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Supramolecular Synthon Frustration Leads to Crystal Structures with Z′ > 1 Kirsty M. Anderson, Andres E. Goeta, and Jonathan W. Steed* Department of Chemistry, Durham UniVersity, South Road, Durham, U.K., DH1 3LE

CRYSTAL GROWTH & DESIGN 2008 VOL. 8, NO. 7 2517–2524

ReceiVed February 8, 2008; ReVised Manuscript ReceiVed April 4, 2008

ABSTRACT: A systematic study into frustration in compounds participating in more than one supramolecular synthon or simultaneously belonging to other categories such as hydrates, co-crystals or crystallizing in a chiral space groups has been undertaken using the Cambridge Structural Database (CSD). The study shows that the combination of more than one directional synthon or the combination of directional synthons with other particular categories of molecule results in markedly increased percentages of structures with Z′ > 1. The majority of combinations show percentages higher than the CSD average of 8.8% and some cases have Z′ > 1 percentages in excess of 60% such as the combination of a carboxylic acid dimer and a molecule in a chiral space group (64.7%). Individual cases have been highlighted and outliers have been discussed and resolved. Introduction 1

Supramolecular synthons based on intermolecular interactions such as hydrogen bonding form the starting point for many crystal engineering studies and are considered by many to be the most important tool currently available to crystal engineers.2–6 Synthon reliability or “robustness” has also proved useful in the field of Crystal Structure Prediction (CSP)7,8 where the validity of predicted structures can be assessed by the presence or indeed absence of particular synthons and hence this can contribute to the ranking order of structures with similar energies.9,10 Motifs such as the carboxylic acid dimer (Scheme 1, 1) are shown to reproducibly form in more than 85% of cases, although this figure drops to 33% when competing donors or acceptors are included.11 It is very likely that combination of one or more competing synthons adds an extra level of difficulty to the crystal structure prediction problem. We have shown that frustration between competing synthons, for example, strongly ionic hydrogen bonding and π-stacking in the case of [(C6H4(NH3)2)2+]8 · (SO4)6 · (HSO4)4 · 8H2O,12 which has eight independent cations, can lead to structures where the asymmetric unit contains more than one molecule (i.e., Z′ > 1).13 Structures with Z′ > 1 have long been of interest to researchers and the topic has enjoyed renewed vigor over the past few years14–19 as computing power and the advent of larger detectors and more powerful X-ray sources has allowed study of structures with increased complexity such as bis(tetraglymeO,O′,O′′,O′′′,O′′′′)-barium(II) bis(iodide) toluene solvate (Z′ ) 8), which has a total of 32 unique molecules in the asymmetric unit (Z′′ ) 32)20 and a unit cell volume of nearly 15 000 Å3.21 Brock et al. have shown that biphenyls containing an hydroxyl group in an ortho position are prone to exhibit high Z′ behavior as the tendency to form a strong O-H...O hydrogen bond needs to be balanced with the difficulties of packing twisted biphenyl fragments in three dimensions.22 We have also shown that more subtle (i.e., weaker) interactions can also be responsible for frustration, namely, in linear X-Au-Y compounds exhibiting Au · · · Au interactions where the driving force to form an Au · · · Au interaction (even at distances > 3 Å) conflicts with steric repulsion between the ligands causing a noncrystallo* To whom correspondence should be addressed. Fax: +44 (0)191 384 4737. Tel: +44 (0)191 334 2085. E-mail: [email protected].

graphic twist between the molecules and hence leading to structures with Z′ > 1 in over 25% of cases.23 We have also shown that steric congestion around the urea group in a series of bis(urea) clathrate compounds leads to disruption (or frustration) of the urea tape motif.24 A striking example of structural frustration is when a chiral molecule is combined with a synthon predisposed to pack around an inversion center, for example, a carboxylic acid dimer. The combination of these two characteristics leads to Z′ > 1 in more than 60% of cases for both carboxylic acid and amide dimers, vastly greater than the average of 8.8% for the Cambridge Structural Database (CSD) as a whole.25 Moreover, close analysis of the structures that do not fit the hypothesis (i.e., chiral molecules containing the synthon but where Z′ ) 1) show that they all adopt C2 symmetry or are difunctional with two independent acid or amide type groups; in other words the distribution of Z′ ) 1 and Z′ ) 2 structures is fully understood with no unexplained exceptions. More recently Bernstein and co-workers26 carried out a statistical survey of the occupation of crystallographic symmetry positions by hydrogen bonded ring motifs and found that the probability of ring formation drops significantly for chiral molecules compared with their racemic or achiral counterparts. There is considerable debate about the origins of crystal structures with Z′ > 1 and a case has been made that all such structures are metastable forms of thermodynamically stable Z′ ) 1 polymorphs, or at least that the Z′ > 1 behavior is a result of the nucleation process.16 While nucleation effects are certainly a factor in the formation of some Z′ > 1 structures we maintain that not only are some Z′ > 1 structures the most stable phase, but in some cases the formation of Z′ ) 1 structures is precluded (or at least any Z′ ) 1 form would be very unstable) by the intrinsic structure of the molecules. Hence explanations of particular Z′ tendencies must be chemically based and structure/ synthon-specific.15 A key aspect in this structural explanation concerns the “frustration” between competing directional interactions or intrinsic structural factors that mitigate against adoption of a packing arrangement compatible with a low Z′. By “frustration” in this context we understand a destabilization of any real or putative Z′ ) 1 structure compared to structures with higher Z′. The word does not imply any instability of the Z′ > 1 forms.

10.1021/cg8001527 CCC: $40.75  2008 American Chemical Society Published on Web 06/13/2008

2518 Crystal Growth & Design, Vol. 8, No. 7, 2008

Anderson et al.

Scheme 1. Categories of Structures Studied, Either Containing Synthons 1-17 or Belonging to Classes 18-20; X is any atom

In this work we aim to analyze the Z′ distribution for 20 commonly occurring categories of compounds (i.e., more than 100 hits in the CSD)27,28 and then compare their individual Z′ tendencies with the proportion of structures with Z′ > 1 when they are combined in a pairwise fashion, resulting in potential frustration. The categories chosen include supramolecular synthons29 such as hydrogen bonded species (1-630 and 1731), halogen-halogen interactions (7-8),32 edge to face and face to face π-stacking interactions (9-10),33–35 hydrophobic long alkane chain interactions (11),36 alkyne · · · alkyne interactions (12),37,38 O-H to alkyne or aryl interactions (13-14),39,40 aurophilic interactions (15),41,42 and 6-fold phenyl embraces (16).43,44 Three other categories are also included: compounds crystallizing in chiral space groups, those containing water, and those with more than one type of chemical residue in the asymmetric unit (Zr > 1),45 for example, cocrystals. It should be noted that Zr is different from Z′′, which represents the total number of crystallographically nonequivalent molecules of whatever type in the asymmetric unit. The parameter Zr is defined as the number of different types of chemical residue (including ions, solvents and other molecules).45 Experimental Procedures The synthons and categories studied are shown in Scheme 1. Further details on exact search parameters can be found in the Supporting Information. For each search carried out a set of refcodes corresponding to positive hits was retained in a file, giving 20 separate files corresponding to the 20 subsets. Each of these files was then compared to the other 19 files using an in-house routine, the main function of which is to compare the two lists of refcodes and output a file containing entries common to both files, that is, refcodes corresponding to structures where both subsets are present. These combined refcode files were then used as the basis for a CSD search (carried out in batch mode) to identify the

Z′ distribution in each combined subset of data. This distribution (as a percentage of Z′ > 1) was then compared to the overall database average for Z′ > 1 which is 8.8% (cf. 11.5% for organic compounds and 6.5% for “organometallic” species).28 It should be noted that when comparing percentages we are merely observing overall trends and not comparing absolute values or apportioning any rigid statistical significance to the data due to the small number of hits observed for some synthon or category combinations. The results of these searches can be found in Table 1.

Results and Discussion Individual Synthons and Categories. The first row of the table gives the Z′ > 1 percentage for each category by itself. Synthons 1-5 are all closely related strongly directional hydrogen bonded ring systems with a tendency to centrosymmetry. Strongly directional intermolecular interactions such as O-H · · · O hydrogen bonds have previously been shown to exhibit a tendency to form structures with Z′ > 1,46–48 and the synthons here are no exception to this rule, with Z′ > 1 percentages ranging from 10.0 to 19.9%. Synthon 6, a more general version of the urea tape motif,24,49,50 is also related to 1-5 as it also has a preference for centrosymmetry, and the percentage of structures including 6 with Z′ > 1 is in line with values for the other categories. While halogen-halogen interactions (synthons 7-8) are not as nearly as strong as conventional hydrogen bonds,30 they do have sufficient directionality to be of use in crystal engineering,51,52 particularly when the donor and acceptor capabilities of the halogens are enhanced.32 This directionality presumably compensates for the weakness of the interaction and that the present data indicates that halogen-halogen bonded species also show an increased tendency to form structures with Z′ > 1. Aromatic interactions represent a different class of species where the directionality of the interaction is greatly reduced

a

14.3 (2371) 1

15.7 (3666) 52.9 (17) 2

2

66.7 (3) 3

19.8 (126) -

3

0 (1) 6

5

4

10.0 (354) 22.2 (9) 3.8 (52) -

6

10.0 (451) 0 (7) 11.1 (9) -

5

19.9 (171) 0 (1) 0 (2) -

4

Number in brackets refers to total number of hits in each subset.

total

1 11.0 (6485) 20.0 (50) 26.9 (67) 100 (1) 0 (3) 0 (3) 50.0 (2) 7

7

0 (9) 8

0 (1) -

-

10.0 (1070) 0 (10) 0 (6) -

8 12.3 (53512) 21.3 (291) 23.8 (303) 45.5 (11) 37.5 (8) 13.9 (36) 25.7 (35) 13.6 (787) 15.4 (54) 9

9

0 (15) 0 (2) 0 (1) 23.4 (47) 0 (1) 11

0 (1) 21.1 (19) 0 (3) 13.3 (143) 10

-

12.4 (846) 13.5 (37) 5.3 (19) -

11

-

-

10.7 (881) 20.0 (5) 50 (4) -

10

0 (2) 41.7 (12) 0 (1) 11.1 (9) 13

26.3 (19) 0 (1) 12

-

-

0 (1) -

-

-

-

-

-

-

-

12.4 (103) 0 (2) -

13

12.8 (133) -

12

100 (1) 14

100 (1) 100 (1) 11.1 (9) 0 (1) 18.0 (217) 50 (2) 0 (1) -

-

15.3 (602) 33.3 (6) 33.3 (3) -

14

15

-

-

-

-

33.3 (9) 0 (1) 25.3 (29) -

-

-

-

20.1 (283) 50 (2) 0 (1) -

15

12.5 (8) 21.4 (14) 16

100 (1) 50.0 (4) 9.2 (87) 0 (6) 9.4 (2728) 0 (3) 0 (1) 100 (1) -

-

7.1 (4648) 0 (8) 10.0 (10) -

16

0 (7) 0 (11) 10.9 (46) 17

-

0 (1) 50 (4) 5.4 (242) 5.6 (18) 12.3 (341) 5.3 (19) 25.0 (8) -

6.2 (5822) 12.5 (24) 2.4 (41) 0 (7) -

17

Table 1. Percentage of Structures with Z′ > 1 for Categories 1-20 Alone (Total) and When the Two Categories Are Combineda

14.8 (73789) 64.7 (139) 56.5 (363) 100 (4) 61.5 (13) 33.3 (21) 18.6 (70) 20.8 (480) 20.9 (67) 19.4 (7588) 36.2 (47) 28.5 (123) 12.5 (8) 33.3 (21) 20.7 (111) 26.7 (15) 23.9 (71) 12.7 (551) 18

18

8.3 (44495) 9.3 (107) 15.8 (417) 14.3 (7) 25.0 (8) 23.8 (21) 14.3 (21) 11.3 (382) 5.0 (40) 13.0 (2867) 9.0 (188) 12.7 (71) 5.9 (17) 13.0 (23) 10.7 (187) 0 (24) 5.7 (246) 6.3 (1257) 15.5 (8992) 19

19

0 (4) 5 (20) 9.7 (31) 8.0 (1327) 4.1 (220) 9.4 (6489) 8.2 (207) 9.2 (87) 7.7 (13) 12.5 (8) 10.1 (138) 15.5 (58) 5.5 (894) 5.2 (1191) 13.8 (7932) 7.7 (27428)

7.0 (56855) 5.8 (104) 9.9 (323) -

20

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2520 Crystal Growth & Design, Vol. 8, No. 7, 2008

compared to the interactions exemplified by 1-8. Nevertheless, edge-to-edge (9), edge-to-face (10) aryl interactions or face-toface alkyne interactions (12) can play an important role in the solid-state packing of many compounds, from polynuclear aromatic hydrocarbons53,54 where interactions between the aromatic regions of the molecule dominate the packing, to structures where the aromatic interactions combine with other inter-andintramolecularinteractionstoformlargearchitectures.55–57 Despite the unpredictability of the geometric interaction and the weakness of the interaction as compared to hydrogen bonds, structures containing aromatic interactions still show an increase in structures with Z′ > 1 compared to the database average. Alkane-alkane synthons are a result of van der Waals interactions and have been utilized in the design of monolayer structures.58,59 It is estimated that the interaction between long chain alkanes can stabilize structures by around 5 kJ mol-1 per -CH2 group, and therefore their contribution to the packing of molecules possessing long alkane chains is significant. Despite their flexibility and large number of possible packing arrangements the percentage of structures containing a long alkane chains which crystallize with Z′ > 1 is still higher than the CSD average at 12.4%. As well as forming π-π type stacking as seen in 12, alkynes can also accept interactions from a variety of hydrogen bond donors such as O-H (13). The OH · · · π(ethynyl) interaction is fairly novel with the first unequivocal evidence for its existence coming from a neutron study of 2-ethynyl-2-adamantanol in 1996,60 which also proved that the donor hydrogen points toward the center of the alkyne bond to form a T-shaped interaction. Similarly, O-H · · · π(aryl) interactions (14) are also known and in fact have been shown to form preferentially over O-H · · · O hydrogen bonds in cases where the OH is sterically hindered.61 The directionality of these interactions ensures that they follow the same pattern as other hydrogen bonded-type synthons, and both exhibit an increased tendency to form structures with Z′ > 1, particularly 14 which is nearly double the CSD average (15.3%). Aurophilic interactions (15) are comparable in strength to hydrogen bonds but do not exhibit the same directionality.41,42 Unusually, despite this lack of directionality they show the strongest preference out of all the categories studied for forming structures with Z′ > 1 (20.1%), more than three times the average value for metal containing species (6.5%). A subset of gold compounds where the gold-gold interaction is between two linear L-Au-L species was studied in detail and was shown to exhibit Z′ > 1 more than 25% of the time. The nature of the ligand was found to be an important factor in the formation of species with Z′ > 1.23 So far we have observed that the tendency to form structures with Z′ > 1 is enhanced for all the intermolecular interactions studied. There are exceptions to this rule, however, namely, the 6-fold phenyl embrace (16) and hydrogen bonds to metal halides (17) which show Z′ > 1 percentages lower than the general database average of 8.8%. The sextuple or 6-fold phenyl embrace (6PE) was initially studied as a supramolecular attraction between Ph3P ligands and consists of a combination of six edge-to-face interactions between phenyl groups,44 but was later extended to include other ligands such as bipyridine, terpyridine, and phenanthroline.43 The 6PE (or 6-fold aryl embrace) has pseudo S6 (3j) symmetry and is observed in a wide variety of structures including metalorganic networks62 and main group complexes.63 The seemingly low percentage of structures with Z′ > 1 is due to the fact that more than 88% of the structures are metal-containing (compared

Anderson et al.

Figure 1. Asymmetric unit of the chiral (S)-(+)-ibuprofen70 showing synthon 5. Hydrogen atoms not involved in hydrogen bonds have been omitted for clarity.

to 1 for example which contains predominantly organic species (∼86%)) and therefore the value is more properly compared to the metal-containing average of 6.5%. Hydrogen bonds involving metal-bound halides (17) have been shown to be similar in length to those to halide anions and to have some directionality with D-H · · · A angles generally between 100-110°.64 The reproducibility of this type of hydrogen bond means that it is a useful synthon for crystal engineers and has been utilized in many metal-halide based crystal engineering studies 65,66 The low proportion of structures with Z′ > 1 compared with the CSD average is again because the subset of data is, by definition, exclusively metal-containing species. The entry for 18 shows the previously observed trend67,68 that chiral space groups have a high percentage of structures with Z′ > 1. Hydrates (19) and the more general class of structures with more than one chemically independent residue in the asymmetric unit (Zr > 1)45 (20) on the other hand show smaller than average percentages of structures with Z′ > 1. This observation can be explained in the following way. If the molecule is not self-complementary69 (i.e., cannot crystallize with Z′ ) 1) then in terms of filling space either it has to include another nonsymmetrical copy of itself (Z′ > 1) or include another completely different residue (Zr > 1). For the latter case formally Z′ ) 1 and hence the percentage of Z′ > 1 will be lower even though Z′′ > 1. While the proportion of structures with Z′ > 1 for the individual classes themselves are of interest, the main thrust of the present study is the effect of combining synthons or categories, leading to frustration. The remainder of Table 1 contains results for combinations of classes which are analyzed below. Combination and Frustration. Some previously observed trends are immediately obvious from Table 1. For example, synthons 1-5 are all predisposed to pack centrosymmetrically and as we have shown previously,25 combination of these synthons with chirality leads to a high proportion of structures with Z′ > 1. This trend is reflected in the present data with high percentages (over 30% in all cases) for all the combinations of 1-5 with 18. Figure 1 shows an example of this combination, namely, the asymmetric unit of (S)-(+)-ibuprofen which crystallizes in P21 with Z′ ) 2.70 While synthon 5 was not explicitly mentioned in our previous work it is pleasing to note that it follows the same trend, albeit with a slightly lower combination percentage with 18, probably because seven of the nine species in this subset contain metals. Examination of the column containing 18 shows that the combination of a chiral space group with any of the other categories leads to increased Z′ > 1 percentages in all cases except for combinations with 12 and 17 which at 12.5 and 12.7%, respectively, are lower than 18 by itself. This again reflects the large percentage of metal containing species in both data sets (100% for 17 and 62.5% for 12).

Supramolecular Synthon Frustration

Crystal Growth & Design, Vol. 8, No. 7, 2008 2521

Figure 2. The asymmetric unit of 1′-(tert-butoxycarbonylamino)ferrocene-1-carboxylic acid71 showing the presence of synthons 1 and 2 which precludes synthon centrosymmetry. Hydrogen atoms not involved in hydrogen bonds have been omitted for clarity.

Figure 4. The asymmetric unit of cis-9,10-diphenyl-9,10-dihydroanthracene-9,10-diol.73

Figure 3. The packing of N-ethylurea19 showing the central urea group participating in synthons 2 and 6 concurrently.

Scheme 2. cis-9,10-Diphenyl-9,10-dihydroanthracene9,10-diols

When two centrosymmetric synthons are combined there is also an increase in structures with Z′ > 1, for example, in structures containing both a carboxylic acid dimer (1) and an amide dimer (2) more than half the structures (52.9%) have Z′ > 1. We believe the large percentage arises from frustration between two strongly directional interactions. As an example, Figure 2 shows the two independent molecules of 1′-(tertbutoxycarbonylamino)ferrocene-1-carboxylic acid.71

In this molecule the top and bottom rings of the ferrocene have different substituents, namely, a secondary amide and a carboxylic acid. According to Etter’s rules,72 and in the absence of other competing hydrogen bond donors/acceptors, the carboxylic acid and amide functionalities would ideally be paired up in homofunctional motifs, and indeed this is what is observed. However, in order to satisfy these two strong, directional interactions the second molecule is unable to orient itself in a fashion compatible with potential space group symmetry operations such as inversion, for example, and hence Z′ ) 2. The high Z′ trend for combinations of centrosymmetric-type synthons is also observed for the 6-fold phenyl embrace (16), which has approximate S6 symmetry, albeit at lower percentages due to the large quantity of metal-containing structures in the data set. Moving on to 6, the urea-tape type motif, we see that combination of this synthon with any of the other synthons or categories of compound gives a larger Z′ percentage than each category by itself, except when the urea tape is combined with 2 when the Z′ percentage drops to only 3.8%. Inspection of this data set shows that in the majority of cases (40 out of 52 structures or 77%) the two synthons are combined around one amide and thus it effectively represents a single synthon rather than a combination, as illustrated in Figure 3 by the structure of N-ethylurea.19 This is in marked contrast to the other combinations where the two synthons are separated by at least one bond. If these 40 structures where the synthons are combined into one “double synthon” are removed from the data set then of the remaining 12 structures, 16.7% (2 structures) have Z′ > 1, in line with the other results. Interestingly, none of the 40 “double synthon” structures have Z′ > 1, and we attribute this to two reasons, first a large percentage of the data set (32.5% or 13 of the 40 structures) have Z′ < 1 (i.e., exhibit molecular symmetry) and second 14 of the 40 structures form a subset of closely related n-alkaneurea compounds and their polymorphs with the general

2522 Crystal Growth & Design, Vol. 8, No. 7, 2008

Anderson et al.

Figure 5. The asymmetric unit of cis-9,10-bis(4-iodophenyl)-9,10-dihydroanthracene-9,10-diol74 showing the presence of synthons 7 (red dashed line) and 9 (black dashed line), O-H · · · O hydrogen bonds not shown.

Figure 6. Part of the crystal packing of 7-ethynyl-6,8-diphenyl-7H-benzocyclohepten-7-ol76 showing the OH · · · C≡C interactions (in red) and the CH · · · π interactions (in black). Hydrogen atoms not involved in these interactions have been removed for clarity (#1: 3/2 - x, -1/2 + y, 1/2 z #2: 5/2 - x, 1/2 + y, 1/2 - z).

formula CnH(2n+1)NHCONH2 (where n ) 2, 5-14)19 which all pack in a similar manner and hence distort the significance of the group. The values for the combination of halogen-halogen interactions (7 or 8) with an M-X...H hydrogen bond (17) are somewhat low (5.4 and 5.8%, respectively) possibly as both interactions are weak and have only limited directionality. The remainder of combinations all give rise to significantly enhanced tendencies to form structures with Z′ > 1, such as the combination between 7 and 2 which has a combination percentage of 26.9%. Despite their reduced directionality, the combination of π interactions (9, 10, or 12) with 7 or 8 also show high Z′ percentages, more than double the value of the individual synthon in the case of the combination of 7 and 10 (21.1% vs 11.0% (7) and 10.7% (10)). A good example of synthon frustration involving halogen bonds and π-stacking as well as

more standard O-H...O hydrogen bonds are the structures of cis-9,10-diphenyl-9,10-dihydroanthracene-9,10-diols (Scheme 2).73,74 When X ) H the molecule crystallizes in P1j with the asymmetric unit consisting of half a molecule with the other half related by symmetry (Z′ ) 0.5).73 Somewhat surprisingly the packing is dominated by OH · · · π interactions rather than O-H · · · O hydrogen bonds (Figure 4), probably due to the steric hindrance of the OH group.47 When X ) Cl74 the molecule changes conformation so that the hydroxyl groups are on the same side of the molecule. The structure packs with four molecules in the asymmetric unit (Z′ ) 4) with the independent molecules held together by a combination of synthons 7 and 9 (Figure 5) as well as conventional O-H · · · O hydrogen bonding. The introduction of a halogen substituent to the phenyl ring causes a large change in both molecular conformation and the packing of these molecules as an extra interaction is added. The X ) Br and X ) I compounds are also known, and when X )

Supramolecular Synthon Frustration

I the molecule does crystallize with Z′ ) 1 but the I · · · I interaction present deviates significantly from linearity (136.63°). When X ) Br75 recrystallization of the compound gives two polymorphs depending on solvent choice. Growth from toluene produces a Z′ ) 4 polymorph, which is isostructural with the chloro analogue, whereas if a trace amount of chloroform is added to the toluene solution a Z′ ) 2 polymorph forms, which, similarly to the iodo analogue, has no linear Br · · · Br contacts, instead O-H · · · O and O · · · Br contacts dominate the packing. The fact that high Z′ structures show a preference for forming cocrystals or in general compounds with Zr > 145 is true for this compound as a chloroform solvate of the Br analogue is also known.75 This 1:1, Z′ ) 1 structure shows no Br · · · Br or Cl · · · Cl contacts. We have already shown that combination of hydrogen bonds and π-π aryl stacking gives rise to structures with high Z′.12 This tendency is reflected in Table 1 for both edge-face and face-face π-π interactions with all combination values being higher than the CSD average of 8.8%, even for the categories containing coordination compounds (16 and 17) and those with Zr > 2 (19 and 20), which show lower than average Z′ percentages in general. The same is true for the π-π alkyne stacking (12), particularly when an alkyne · · · alkyne interaction is combined with an edge · · · face π interaction (26.3%). The combination of edge-face π-interactions (9) and OH · · · C′C (13) interactions is particularly high at over 40%. A good example from this subset is the structure of 7-ethynyl-6,8diphenyl-7H-benzocyclohepten-7-ol76 which has synthons 9 and 13 present and crystallizes with Z′ ) 2 (Figure 6). OH · · · π interactions (14) show similar tendencies to form structures with Z′ > 1 as 9, particularly when combined with an edge-face π-stacking motif (9). Hydrophobic interactions between aliphatic chains (11) are also a source of intermolecular frustration with increased Z′ > 1 percentages for the majority of combinations. Combination of 11 with 2 and 6 give low percentages (5.3% and 0%, respectively), closer examination of these data sets show that these two combinations are dominated by a subset of the n-alkaneurea19 compounds seen in the “double-synthon” combination of 6 and 2. The 10 compounds (5 unique compounds and a number of polymorphs) represent over half the group in both cases and hence skew the percentage. Combination of an aurophilic interaction (15) with nearly all the other categories of molecule leads to increased Z′ > 1 percentages except in the case of hydrates where none of the 24 structures has Z′ > 1. Inspection of this data set revealed that 6 of the 24 structures have asymmetric units, which, due to the vagaries in the Z′ nomenclature,77 could be classified as Z′ > 1,23 taking this into account the “real” Z′ > 1 percentage is closer to 25% and thus is as expected. The data set of metal chlorides as hydrogen bond acceptors (17) somewhat bucks the trend of the other synthons in this study, possibly because metal halides are poor acceptors compared to NH and OH groups as seen in other synthons.64 Also hydrogen bonds involving metal halides are not as directional as stronger hydrogen bonds, and therefore some flexibility in the approach of the hydrogen atom may be possible, hence making symmetrical interactions between molecules more likely. Conclusions The large variety of categories of structures contained in this study shows that the interplay between molecular fragments can be altered dramatically on addition of a further competing

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interaction, or by changing the fundamental characteristics of the structure by making the structure chiral or by introducing additional molecules into the lattice. We have investigated the trend for individual synthons or categories of molecule and have also shown that a combination of two or more of these synthons or categories, each with their own particular intrinsic structural tendencies, generally increases the percentage of structures formed with Z′ > 1, in some cases to more than 50%. This study thus conclusively shows that frustrating packing demands can arise from intrinsic chemical classes across a broad spectrum of structures, and are not exclusively a result of kinetic crystal nucleation phenomena. Acknowledgment. We would like to thank the EPSRC for funding. Supporting Information Available: Details of exact CSD searches carried out. This information is available free of charge via the Internet at http://pubs.acs.org.

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