Bimodal Distribution of the Shortest Intermolecular Contacts in

Article pubs.acs.org/crystal

Bimodal Distribution of the Shortest Intermolecular Contacts in Crystals of Organic Compounds Michał Kaźmierczak and Andrzej Katrusiak* Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland ABSTRACT: There are clearly two maxima in the distribution of the shortest intermolecular contacts, referred to the atomic van der Waals radii, in crystals of organic compounds. Accordingly, the crystals of organic compounds can be classified into those governed by strong cohesion forces (such as OH···O, NH···O, and NH···N hydrogen bonds) and weak ones (CH···O, CH···π, halogen bonds, and dispersion forces). In about 1/3 of all known structures of organic compounds, there are strong cohesion interactions, while in 2/3 of structures the shortest contacts are associated with weak interactions. Characteristic properties of organic compounds depend on these either strong or weak cohesion forces. The distributions of the shortest intermolecular contacts of specific types, such as OH···O, NH···O, CH···N, and Br···Br can be approximated by the Gaussian functions. These Gaussian functions, with mean distance and standard deviation characteristic of specific interactions, can be used for predicting molecular arrangements and for validating crystal structures.

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INTRODUCTION The rules governing the formation of crystal structures of organic compounds were studied by various methods.1−4 The effects of molecular packing in crystals, symmetry, and interactions are considered to be the most important factors. The cohesion forces of different types are essential for calculating the crystal stabilizing energy and for predicting the crystal form and properties at normal5,6 and extreme conditions.7,8 A comprehensive description of crystal structures requires that the concepts of close packing and of weak interactions, like those involving CH groups9,10 and halogen atoms,11,12 be considered. The knowledge of cohesion forces in the crystals is vital for understanding the general rules governing the molecular aggregation and the structure− property relations in functional materials and natural systems. All this knowledge is generally applied in materials and structural chemistry, as well as in chemical practice. The detailed description of all cohesion forces and their distribution in crystals requires that weak interactions be analyzed separately from stronger interactions, which are very likely to bias the effect of weaker interactions under study. Usually, the shortest of intermolecular and interionic contacts, related to the sum of van der Waals radii of the involved atoms, is associated with the strongest cohesion interaction in the crystal structure of an organic compound. Furthermore, the vast variety of chemical compounds deposited in crystallographic databases suggests that the shortest intermolecular contacts in crystals correspond to specific types of the strongest cohesion forces. On the other hand, these forces are responsible for the molecular aggregation. Most recently, we established that there are crystals with all intermolecular distances in their structure longer than the sum of van der Waals radii.13−15 Such crystals have been called loose crystals, and they illustrate the role of cohesion forces for molecular aggregation. This observation was © 2014 American Chemical Society

connected with particularly weak cohesion forces often characteristic of volatile compounds, but loose crystals were found also among compounds that are stable and solid at normal conditions.13,16 Presently we have extended our study of the shortest intermolecular contacts in organic and metalloorganic compounds to the whole range of distances, from the longest ones, as in loose crystals, to the shortest, approaching covalent bonds. For this purpose, we have extracted the shortest contacts relative to van der Waals radii of atoms in all structures deposited in the Cambridge Structural Database (CSD) and derived distributions of the shortest intermolecular distances. We have searched the CSD (version 5.34, released in November 2012;17 ConQuest, version 1.1518) for the shortest intermolecular contacts, as related to the sum of atomic van der Waals radii of atoms involved. For this purpose, in each structure, of all differences between intermolecular or interionic distances and the van der Waals radii of the involved atoms, the smallest value was found and defined as parameter δ for this structure. The method of this search and its criteria were described previously.13 For each structure, the shortest intermolecular contact δ has been found according to the following formula: Λ(dij ∈ D)(δ ≤ dij − vdWi − vdW) j

(1)

where Λ indicates the universal quantifier, dij are intermolecular distances between atoms, D is the set of all intermolecular contacts between atoms, and vdWi and vdWj are the van der Waals radii according to Bondi19of the ith and jth atoms, Received: December 2, 2013 Revised: March 25, 2014 Published: April 2, 2014 2223

dx.doi.org/10.1021/cg4018008 | Cryst. Growth Des. 2014, 14, 2223−2229

Crystal Growth & Design

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respectively. For all structural models, the positions of H atoms were normalized using bond lengths determined by neutron diffraction (C−H 1.089 Å, N−H 1.015 Å, and O−H 0.993 Å).20 The histogram of the shortest-contact parameters δ derived from all CSD structures is shown in Figure 1.

Figure 2. Histogram of the shortest NH···N contacts in the CSD (in δ steps of 0.02 Å). The outlier H···N contact yielding δ = −1.28 Å (indicated by the black arrow) in ammonium hydrogen urate ammonia, excluded from further analysis due to the distorted uricacid molecule (the dihedral angle between the ring planes of 147.23°).17 The inset shows a projection of the deposited model.

III and IV. It turned out that all entries of peak IV (δ ≈ −2 Å) are covalent or coordination bonds interpreted by the Conquest search procedure as intermolecular contacts. Such entries have been discarded from further analyses. Peak III (δ ≈ −1.5 Å) contains mainly the structures of MOFs and catenas (presently about 21000 entries in the CSD), where the shortest contacts involve an oxygen atom and metal cations (Na+ or K+ etc.). Structures with such short intermolecular distances have been excluded from further analysis, too. Most of the remaining 331 entries, falling into the broad peak III, were associated with short OH···O (312 structures) and NH···N (19 structures) hydrogen bonds, where the proton is located at a symmetry element, like the inversion center Ci in 203 structures and the 2-fold axis C2 in 72 structures. The δ value in such OH···O bonded structures forms a much sharper peak at about −1.5 Å (Figure 3). These structures have been discussed separately in the discussion paragraph dedicated to hydrogen bonds OH···O. These 331 structures within peak III are much less numerous than the main features of the δ-distribution, which are peaks I and II (Figure 3). The remarkable result of this survey is that almost all crystal structures deposited in the CSD can be discriminated according to their δ parameter value into two groups, corresponding to peaks I and II of the histogram in Figure 3. Peak I contains nearly 2/3 of all deposited structures. Their average δ value (δ̅ = N−1∑δj, where N is the number of structures and δj, j = 1, ..., N, are their δ values) is −0.31 Å, and the scatter parameter, defined as standard deviation σ = [N−1∑(δ − δ̅)2]1/2, is 0.12 Å. The average δ of peak II, consisting of over 1/3 of CSD deposits, is −0.86 Å with the scatter parameter of 0.18 Å. Thus, the most populated peak I is sharper, and the less populated peak II is broader by about 50%. The height and width of peaks I and II reflect the variety of chemical functional groups involved in the strongest interactions in the crystal structures. The contributions of intermolecular contacts involving H atoms to the δ-histogram peaks I and II are shown in Figure 3. It includes component distributions of contacts H···H, C···H, N···H, O···H, and X···H (where X stands for a halogen atom, F, Cl, Br, and I). These are the most frequent shortest contacts in the deposited crystal structures (98% of all entries). The O···H contacts are clearly

Figure 1. The histogram of CSD-structure distribution as a function of parameter δ (in δ steps of 0.02 Å). The Roman numbers label the peaks from the largest δ values (peak I corresponds to the longest contacts) to the smallest δ values (peaks II, III, and IV).

Like in the previous survey,13 considerable care had to be taken to verify the entries. Fortunately, it occurred that the magnitude of the δ parameter, compared with its expected value for a specific type of interactions, is an efficient method of validating structural models. In this way, several groups of most common errors in deposited structures were detected previously. However, two additional types of errors have been identified in this study. (1) Unexpectedly small values of parameter δ can indicate errors in molecular geometry, which can be further reflected in unrealistic intermolecular distances. For example, the smallest δ parameter of −1.28 Å was found for hydrogen bond NH···N in the structural model of ammonium hydrogen urate ammonia (HOZSUL),21 where the molecule of uric acid is considerably distorted from the chemically reasonable flat conformation (Figure 2). There are several structural models containing water molecules with unexpected geometry, such as the H−O−H angle of 171.93° in GUMSIQ22 and 172.25° in WOGGUU.23 These molecular-geometry distortions lead to exceptionally short intermolecular contacts. Such dubious δ parameters were excluded from the δdistribution analysis. (2) The location of H atoms in hydrogen bonds becomes crucial for identifying the smallest δ value. This concerns very many OH···O bonds with the H atom assigned to the midpoint position between the oxygen atoms, as in COJRUP24 or SOBPIJ.25 This problem will be discussed later below.

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DISCUSSION It can be observed that the histogram in Figure 1 contains clear features of peaks I and II and considerably less populated peaks 2224



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Figure 4. The bimodal δ-distribution of the shortest contacts (the white shape; cf., Figure 1), with the bimodal component δ-distribution of O···H contacts (purple), further decomposed into unimodal δdistributions of contacts CH···O (blue), NH···O (red), and OH···O (orange), all plotted in δ steps of 0.02 Å.

Figure 3. Five most populated types of the shortest contacts in the CSD structures plotted as a function of parameter δ (in δ steps of 0.02 Å): H···N (orange), H···H (lime), H···X (blue; X = F, Cl, Br, and I), H···C (black), and H···O (purple). The white shape represents the histogram after excluding MOFs, catenas, and deposits with apparent structural errors (cf. Figure 1).

contacts OH···N and NH···N in peak II, followed by the peaks representing contacts CH···N in peak I. This sequence corresponds to the decreasing electronegativity of atoms covalently bonded to the H atom (Figure 5). It can be shown (Figure 6) that contacts CH···X constitute nearly all δ-parameters of contacts H···X within peak I (Table 1). Contacts NH···X and OH···X form very broad distributions with their shorter shoulder extending to −1.0 Å in peak II. In Figure 7, the δ-distribution of contacts NH···X have been further decomposed into δ-distributions for contacts NH···Cl (the most populated and shortest), NH···Br, NH···F, and NH···I (the least populated and longest). Most of the δ-values of contacts NH···I fall into the region of peak I, while most of other δ(NH···X) values are located in the gap between peaks I and II. The peak of δ(NH···X) values is much more populated and broader than the δ-distribution for contacts OH···X (Figure 6). Peak δ(CH···X) is relatively narrow (σ = 0.114 Å, Table 1), considering the low energy of corresponding CH···X interactions. It contrasts with considerably broader δ-peaks of contacts OH···X and NH···X, with the scatter parameters σ equal to 0.1326 and 0.1817 Å, respectively. This exceptionally broad δ-distribution for the NH···X contacts, extending between peaks I and II, is due to the considerably different δ̅ means for contacts NH···F, NH···Cl, NH···Br, and NH···I (Figure 7, Table 1). It appears most surprising that contacts NH···I are the longest in this comparison, somewhat shorter are contacts NH···F and then NH···Br, and the shortest are contacts NH···Cl. However, it will be shown later that iodine atoms favorably form short I···I contacts; hence contacts H···I are less likely. Contacts NH···Cl are also most frequently represented among the shortest NH···X contacts, which is consistent with their significant role in molecular aggregation and with the chlorophobic effect noted by Zorky and Griniewa.26 Similarly to other contacts, the δ-distribution of hydrogen bonds can be described by the Gaussian function (Table 1; eq

distributed between peaks I and II with similar frequencies and constitute the largest bimodal-component δ-distribution. The other types of contacts are mainly located in peak I, except for the much less frequent N···H contacts, approximately equally distributed between peaks I and II. It is noteworthy that the δdistribution of contacts X···H is mainly represented within peak I, but a much less populated component of this distribution extends into peak II. Figure 4 further decomposes the most-populated bimodal component O···H δ-distribution (cf. Figure 3) into CH···O, NH···O, and OH···O unimodal subcomponent δ-distributions. In this group, most frequent are CH···O contacts almost fully located within peak I. The CH···O contacts also constitute nearly the full contribution of O···H contacts to peak I. In turn, most hydrogen bonds of OH···O and NH···O fall into peak II. The distributions of these contact types are quite regular and can be approximated by the Gaussian-type function ⎛ (δ − δ ̅ )2 ⎞ G(δ ̅ , σ ) = h exp⎜ − ⎟ 2σ 2 ⎠ ⎝

(2)

where h is the maximum of function (corresponding to the maximum frequency of δ), δ̅ is the average δ, and σ is the standard deviation of the distribution. Function G(δ̅, σ) has been fitted to the distributions of specific contacts types. Thus, different contacts types can be characterized by the statistical parameters δ̅ and σ of their Gaussian functions fitted to the δ distributions (Table 1). There is a clear difference between average parameter δ̅ of contacts OH···N and NH···N, −0.9166 and −0.7133 Å, and between their scatter parameter σ, 0.118 and 0.1419 Å, respectively. Three main components of the δ-distribution of N···H contacts are the subdistributions of interactions CH···N, NH···N, and OH···N. As was observed for the δ-distribution of contacts O···H, the most negative values of δ̅ correspond to the 2225



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Table 1. Parameters Describing the Gaussian-Function Fitted to Peaks I and II and to Component δ-Distributions of the Most Frequent Types of Contacts in δ Steps 0.02 Åa peak

δ̅ [Å]

σ [Å]

h

R

fwhm [Å]

I II H···H CH···O NH···O OH···O CH···N NH···N OH···N C···H CH···X NH···X OH···X CH···F NH···F OH···F CH···Cl NH···Cl OH···Cl CH···Br NH···Br OH···Br CH···I NH···I OH···I CH···S NH···S OH···S S···S F···F Cl···Cl Br···Br C−I···I−C I−I···I−I

−0.3117 −0.8792 −0.2862 −0.3331 −0.8135 −0.9535 −0.2895 −0.7133 −0.9166 −0.2594 −0.3013 −0.6874 −0.7768 −0.3414 −0.6287 −0.8861 −0.2867 −0.7264 −0.7981 −0.2642 −0.6759 −0.7334 −0.2262 −0.4981 −0.6181 −0.2588 −0.5739 −0.6975 −0.2521 −0.1756 −0.1461 −0.1886 −0.1614 −0.4254

0.1166 0.1741 0.114 0.1083 0.1395 0.1146 0.1011 0.1419 0.118 0.0927 0.114 0.1817 0.1326 0.1103 0.2019 0.1913 0.1052 0.1628 0.111 0.1041 0.1367 0.0993 0.1021 0.1317 0.0615 0.0969 0.1095 0.0967 0.102 0.1058 0.1179 0.1290 0.0858 0.1482

14730.5 5155.1 4338.0 5627.7 2187.2 2839.7 727.3 388.3 446.1 2865.1 1870.3 368.5 178.7 759.1 48.1 18.1 903.4 264.1 134.8 206.1 68.4 40.8 120.5 28.6 21.9 349.8 146.0 21.1 41.7 200.7 136.1 79.9 27.4 27.3

0.9979 0.9979 0.9955 0.9995 0.9919 0.9943 0.9978 0.9932 0.9975 0.9988 0.9996 0.98 0.9951 0.9989 0.9774 0.9274 0.999 0.9656 0.9932 0.9939 0.9714 0.9848 0.9962 0.9736 0.9682 0.9991 0.9877 0.9661 0.9745 0.9976 0.9839 0.9831 0.9622 0.9953

0.275 0.41 0.268 0.255 0.328 0.263 0.238 0.334 0.278 0.218 0.268 0.428 0.312 0.26 0.475 0.45 0.248 0.383 0.261 0.245 0.322 0.234 0.24 0.31 0.145 0.228 0.258 0.228 0.24 0.414 0.344 0.444 0.38 0.349

Figure 5. Bimodal δ-distribution of N···H (orange) contacts decomposed into unimodal δ-distributions of contacts CH···N (willow-yellow, all within peak I), NH···N (red), and OH···N (dark red, peak II). The white shape represents the δ-distribution of all CSD structures (in δ steps of 0.02 Å; cf. Figure 3). The vertical dashed line projects the gap minimum between peaks I and II.

δ̅, mean value; σ, standard deviation; h, peak height; R, least-squares fit coefficient of the G(δ̅, σ) function to the δ-distribution; fwhm, the full width at half-maximum of the δ-distribution. a

Figure 6. Contributions of δ-distributions of specific interaction types in the population of contacts H···X, plotted in δ steps of 0.02 Å. The vertical dashed line projects the gap minimum between peaks I and II.

2). The δ-distribution for NH···N bonds has been shown in Figure 5. The smallest δ-value contained in the δ-distribution of the N···H contact of 1.636 Å is that in the structural model reported for the trialkylammonium-trialkylamine-tetraphenylborate crystal (refcode YERLOW).27 In other deposited structural models, there are still shorter NH···N contacts; however they are highly unlikely. In this case, all outliers of the δ-distribution were considered as an indication of errors. Presently in the CSD, there are 12 deposited structures containing NH···N contacts shorter than that in YERLOW. Our inspection of these 12 entries revealed errors in the deposited models. For example, in the crystal of catena-(4,4′bipyridylium(μ2-4,4′-bipyridyl)-tetrabromo-bismuth(III))28 the N···N distance of 2.32 Å and NH···N distance of 1.337 Å (refcode CEDDIZ; Figure 8) between 4,4′-bipiridium cations is most likely due to errors caused by very high absorption of this compound (μCuKα = 14.87 mm−1) and to very weak scattering of X-rays by light atoms compared with the strong X-ray scattering by bismuth. Another outlier with unexpectedly short N···N distance (2.44 Å) is the structural model of

tetraammonium bis(μ5-oxo)-tetrakis(μ3-oxo)-hexakis(μ2-oxo)tetradecaoxo-octa-molybdenum hexakis(4,4′-bipyridine) (refcode XIJGIG),29 where errors are additionally indicated by strongly deformed pyridine rings. The halogen−halogen bonds form a unimodal δ-distribution with a short δ shoulder, all within peak I (Figure 9). The δhistogram for contacts I···I contains the contributions of iodinesubstituted hydrocarbons, as well as the contacts between polyiodide ions. The former contact is shifted to right and the latter to left, which is the reason for bimodal distributions of I··· I and X···X halogen contacts. Most of the δ-values of these contacts are contained within peak I; however there are few shorter contacts. The inspection of the structures with parameter δ smaller than −1.0 Å showed that there are errors in these models. These unexpectedly short halogen−halogen contacts all can be due to disordered solvent molecules (i.e., 2226



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Figure 7. Contributions of δ-distributions for specific interaction types in the population of contacts NH···X (in δ steps of 0.05 Å). The vertical dashed line projects the gap minimum between peaks I and II.

Figure 9. The δ-distribution of halogen···halogen contacts (δ steps of 0.1 Å). The X···X δ-distribution includes both homo- and heterohalogens contacts F···F, F···Cl, F···Br, ..., I···I. The vertical dashed line projects the minimum of the gap between peaks I and II (cf. Figure 3).

than those in the Gaussian δ-distribution GS···S(−0.24; 0.10). The δ values for these shorter contacts are between −1.00 and −0.68 Å. We have closely examined and validated all these structural models, and no objections regarding their determination and presentation could be found. We established that in these ten structures with exceptionally small δ-contact, the sulfur atom is covalently bonded to strongly electronegative atoms, which is consistent with the literature information that sulfur atoms in such an electronegative environment are capable of forming very strong intermolecular interactions. According to the δ-histogram (Figure 1), these 10 contacts classify as peak-II contacts. The small number of specific types of δ-values (for example, those representing short S···S contacts) can raise concerns that contacts types underrepresented in the CSD may blur the overall δ-distribution (Figure 1) and that it may bias the classification of crystals based on the δ-values. The S···S contacts have been used below for clarifing this point. The present survey is based on the limited probe of crystal structures deposited in the CSD, and it can be considered (i) why some of the contact types are so few and (ii) how the number of the δ values compare with the number of similar contacts of the same type, but not the shortest one, in the crystal structure. For example, in the crystal structure of perfluorodibenzo(c,g)-1,2,5,6-tetrathiocin (BIBKUS01)33 the smallest δ value of −0.382 Å corresponds to the S···S contact of 3.218 Å. However, in the crystal structure of thiobarbituric acid (THBARB0234), a shorter S···S contact of 3.128 Å would not yield a δ-value of the S···S type, because there are other contacts (H···O) yielding a smaller vdW-radii referenced δ parameter equal to −0.847 Å. Thus, this δ-value of type H···O is included into the δ-distribution. Only the shortest vdW-radii referenced distance in a crystal structure is denoted as δ, and all other vdW-radii referenced distances in this structure will be denoted as δ′ in the further discussion. Thus, in the latest example of refcode THBARB02, the δ value is −0.847 Å, and

Figure 8. Histogram of distances N···N in NH+···N bonded chains of 4,4′-bipiridine monosalts (gray area; in steps of 0.1 Å) and a Gaussian function fitted to these N···N distances (red). The black arrows indicate the outlier structures of catena-(4,4′-bipyridylium(μ2-4,4′bipyridyl)-tetrabromo-bismuth(III)), refcode CEDDIZ,28 and tetraammonium bis(μ5-oxo)-tetrakis(μ3-oxo)-hexakis(μ2-oxo)-tetradecaoxoocta-molybdenum hexakis(4,4′-bipyridine), refcode XIJGIG.29 The N···N distances in 4,4’-bipiridine monosalts are at the shortest range of δ-distribution GNH···N (Table 1).

CH2Cl2), disordered anions (either simple ones, like Br−, or complex ones, like PF−6 ) and disordered halogen-substituted methyl groups. The halogen bonds can be described as σ−hole interactions, which generally can involve atoms of groups IV−VII and electronegative atoms.30 Of like−like contacts between atoms S, P, Se, and As, particularly intriguing are possible applications of interactions S···S in crystal engineering31 and their role for the reconfiguration of S−S bridges in proteins.32 Most of the S···S contacts fulfilling criterion 1 for the δ values fall into the region of peak I and form a regular Gaussian δ-distribution GS···S(δ = −0.24; σ = 0.10 Å), as shown in Figure 10. However, there are ten δ-parameters of contacts S···S significantly shorter 2227



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peaks I, II, and III can be equally applied to the molecules, compounds, crystals, and interaction types. The weak interactions exist between H···H, CH···N, CH···O, and most of halogen−halogen atoms. The strong interactions are two times less frequent, and they comprise mainly hydrogen bonds OH···O, NH···O, and NH···N, as well as somewhat weaker (with distances closer to the gap) hydrogen bonds NH···X and OH···X (X denotes halogen atoms, F, Cl, Br, or I). The δ̅ value can be used for assessing the strength of interactions. For example, NH···Cl contacts have on average their δ smaller than contact NH···I. However, these are statistical distributions, which can be biased by different groups of compounds. For example, perfluorinated molecules form stronger halogen bonds than the not-fluorinated analogues.38 The outliers of the Gaussian distributions of contacts should be carefully inspected. We have found that such δ outliers are often due to errors in the deposited structural data. On the other hand, the example of the smallest S···S δ-parameters shows that outliers may be due to an ‘exotic’ type of intermolecular contact underrepresented in the CSD. The δ parameter provides qualitative and quantitative means of assessing the effects of different types of cohesion forces between molecules in the aggregates and in crystals. However, general conclusions of δ-distributions should be applied with care for specific functional groups, because their ability to interact and aggregate depends on the molecular and crystal structure, as was demonstrated for “shielded” −OH groups unable to form hydrogen bonds.39 Presently, practical applications of the classifications of structures basing on δdistribution are being further investigated.

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Figure 10. (a) The δ-distribution of S···S contacts plotted with δ steps of 0.05 Å. The yellow histogram includes all δ-values of S···S type, and the black Gaussian curve is fitted to all these data; the blue curve was fitted to the data larger than −0.68 Å (the right side of the gap); the vertical dashed line projects the minimum of the gap between peaks I and II (cf. Figure 3). (b) Selected structures illustrating the variety of S···S contacts and their δ values.33,35−37

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

The Foundation for Polish Science, Team Grant 2009-4/6. Notes

The authors declare no competing financial interest.

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the vdW-referenced value of the shortest S···S contact is δ′S···S equal to −0.472 Å. The GS···S(−0.24; 0.10) δ-distribution in Figure 10 includes 585 structures, whereas there are 7075 structures with δ′S···S < 0 Å, 1267 of them with δ′S···S < −0.25 Å. Presently, in the CSD, there are ten structures with δ < −0.68 Å, that is, beyond the shorter side of the GS···S(−0.24; 0.10) distribution (coinciding with the gap between peaks I and II). However, there are 48 structures with δ′S···S < −0.68 Å (i.e., there are 38 structures where such short S···S contacts are present, but there are still shorter δ-contacts in these structures). Thus, it can be concluded that structures with the shortest S···S δ-contacts clearly form a separate type lying outside the GS···S(−0.24; 0.10) distribution. However, these δS···S structures are still too few (presently deposited in the CSD) for forming a separate Gaussian distribution.

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CONCLUSIONS It has been established that the contribution of δ-distribution, corresponding to the shortest intermolecular contacts in crystal structures determined until now (and deposited in the CSD), allows organic compounds to be classified as those aggregating with weak (peak I) and strong (peaks II and III) interactions. The clear division between the crystal structures grouped in 2228



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Bimodal Distribution of the Shortest Intermolecular Contacts in

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