Crystal Growth & Design - ACS Publications - American Chemical

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It Isn’t, It Is: The C−H···X (X = O, N, F, Cl) Interaction Really Is Significant in Crystal Packing Robin Taylor* Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, U.K. S Supporting Information *

ABSTRACT: Arguments about the importance or otherwise of the interaction between a C−H group and an electronegative atom such as oxygen, nitrogen, or halogen have rumbled on for 50 years or more. The latest contribution to the debate, published recently in this journal, tended to downplay the significance of the interaction. However, a comparison of observed interaction frequencies with those expected from surface area considerations sheds a different light on the matter.

INTRODUCTION Thirty-four years ago I published a paper with Olga Kennard on C−H···O, C−H···N, and C−H···chloride hydrogen bonds.1 (I distinctly remember the day I started on the project. Prince Charles was marrying Lady Diana in St Paul’s Cathedral, and it was a public holiday in the United Kingdom, but as an avowed antimonarchist I put my hair shirt on and went to work. At least it was quiet.) While I was aware that the topic was controversial, I did not realize that it was practically taboo to use the term “hydrogen bond” for these interactions. Olga probably knew but decided not to scare her naive postdoc by sharing the information. Anyway, the paper was accepted but somewhat grudgingly, one of the referees suggesting that the interactions should be termed “sutors” rather than hydrogen bonds. This was a reference to June Sutor, who was the first to propose, in 1962, that at least some C−H···O contacts in crystal structures should be regarded as hydrogen bonds.2 Her views had been roundly dismissed by Donohue, who posed the rhetorical question “The C−H···O hydrogen bond: what is it?” and answered “It isn’t”.3 Our paper supported Sutor’s position. Very soon, others, notably Desiraju, took the same view,4−7 and Bernstein concluded in 2013 that “it certainly is”.8 However, there has never been a total meeting of minds on the issue.9−11 Of the evidence that Olga and I presented, the most convincing to me was the systematic nature of the C−H groups that formed short contacts to electronegative atoms: they were invariably in electron-withdrawing environments, making the hydrogen atoms unusually acidic. It was hard to believe that these contacts were random artifacts of crystal packing. And for the next 30 years, I held the view (perhaps I should say prejudice) that it was only this type of C−H group that formed worthwhile hydrogen bonds. For example, I did not think that the methyl hydrogens at the end of an alkyl chain could form © XXXX American Chemical Society

C−H···O interactions of any significance. I also doubted the importance of C−H···F and C−H···Cl contacts when the halogen was covalently bonded to carbon. Others disagreed12−15 and a couple of years ago I decided to prove them wrong. My idea was to consider many different types of interatomic contacts and establish which occurred significantly more often in crystal structures (that is, significantly in a statistical sense) than would be expected by chance. To my surprise, the results indicated that contacts such as methyl···O, C−H···F−C, and C−H···Cl−C are all comfortably overrepresented in organic crystals compared to what would be expected at random.16 I was converted. So I was surprised by a recent paper by Gavezzotti and Lo Presti (henceforth, G&LP).17 They studied four data sets retrieved from the Cambridge Structural Database (CSD),18 each consisting of crystal structures containing molecules with only C, H, and X atoms, where X = O, N, F, or Cl. Statistical analyses of the structures were performed, along with latticeand dimerization-energy calculations using the highly respected PIXEL program.19 The focus of their statistical analysis was almost exclusively on intermolecular contacts shorter than the sum of the van der Waals (vdw) radii of the atoms involved (G&LP prefer the term “standard atomic radii”). Among their findings were (1) the lattice energies of the structures are largely dominated by dispersion; (2) short C− H···O contacts are very frequent, short C−H···N contacts are less common though still numerous, but (my italics) short C− H···Cl and C−H···F contacts are sparse or just sporadic; (3) molecule−molecule interaction energies are not usually dominated by C−H···X Coulombic contributions, even when Received: May 15, 2016


DOI: 10.1021/acs.cgd.6b00736 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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there are short C−H···X contacts between the molecules. In their conclusions, G&LP remarked that the contacts made by X atoms at the threshold of the sum of atomic radii “show a multiform and nonspecif ic coordination with many donors, suggesting that only really shorter contacts are worth considering”. (This conclusion seems at variance with the assertions of several authors that weak hydrogen bonds may often be longer than the sum of vdw radii yet still be significant.7,20) They also concluded that C−H···O and C−H···N can be influential in determining crystal structures but only when very short and especially in small molecules, and that the relevance to crystal packing of C−H···Cl and C−H···F contacts “seems to be more an exception than a, however weak, rule”. G&LP’s conclusions are clearly in opposition to my newly adopted viewpoint. One criticism that can be leveled at their analysis of contact frequencies is that they did not know how commonly the various types of contacts would be expected to occur if packing were random. This obviously depends on stoichiometric factors and also, as they noted, on the steric accessibility of atoms. It is precisely these factors that the procedure used in my 2014 paper aims to quantify.16 However, that study was done on a very diverse set of crystal structures, whereas G&LP’s structures fell into tightly defined chemical subsets, each containing only three elements. Perhaps this made a difference? I could not resist investigating.

RF(A ··· B) = ΣO(A ··· B)i /ΣE(A ··· B)i


where the summations are over the crystal structures, O(A···B)i is the observed number of A···B primary interactions in the ith structure, and E(A···B)i is the expected number. Surface areas were computed using the method of Infantes and Motherwell.22 The 95% confidence interval for RF(A···B) was estimated by bootstrapping.16 In the main part of the study, RF values were determined for the three possible types of primary interactions that X atoms can form (X···H, X···C, and X···X) in the four G&LP data sets. Since the results depend on the radii assumed for the atoms, all calculations were performed in triplicate, using the radii of G&LP (which are those of Rowland and Taylor23), those of Alvarez,24 and those of Bondi.25 As expected, the choice of vdw radii has a small effect on the RF values, but the conclusions of the study remain valid whichever set of radii is used. To aid comparison with G&LP, the discussion below is based on the results using their radii.

RESULTS Table 1 gives RF values and their 95% confidence intervals for X···H, X···C, and X···X primary interactions with Δ ≤ 1.0 Å. All Table 1. RF Values for X···H, X···C, and X···X Primary Interactions with Δ ≤ 1 Å, where X = O, N, F, and Cla


Data sets. The CHO, CHN, CHF, and CHCl data sets of G&LP were used, but structures with missing hydrogen-atom coordinates were rejected, leaving 875, 428, 115, and 197 structures, respectively. A fifth data set, CHOF, was set up by searching the CSD with standard software (ConQuest21) for structures satisfying the following conditions: contain C, H, O, and F atoms, no other elements, and at least one carbonyl group; coordinates available for all atoms, including hydrogens; R-factor ≤5%; Z′ ≤ 1; no disorder; no structures marked in the CSD as being in error; no polymers; no powderdiffraction structures; no ions. This data set comprised 600 structures (CSD reference codes deposited as Supporting Information). Following the procedure of G&LP, all hydrogen atoms were moved along their valence-bond directions to make the bond lengths equal to average neutron-diffraction values. Molecular Interactions. The study was based on interatomic interactions obeying the following conditions: (a) intermolecular; (b) line-of-sight, i.e., the interacting atoms “see” each other because no third atom intrudes between them;16 (c) Δ < 1 Å, where Δ is the interatomic distance minus the sum of the atoms’ vdw radii. Except where otherwise stated, a maximum of one interaction per crystallographically independent atom was considered, namely, the one with the smallest value of Δ (thus, the shortest interaction after correction for vdw radii). This is termed the atom’s primary interaction. In one part of the study, secondary and tertiary interactions were also included, these being the interactions with the second and third smallest values of Δ. It is possible, of course, that an atom might not form three line-of-sight interactions that satisfy the limit on Δ, in which case there may be no tertiary, secondary, or even primary interaction for that atom. The RF Metric. Consider an atom of a given type, A, in a crystal structure containing atoms of types A, B, C... If packing were random, the probability that the atom would form its primary interaction to an atom of type B would be SB/Stotal, where Stotal is the total surface area of the molecule(s) in the asymmetric unit and SB is that part of the surface area corresponding to atoms of type B. Suppose there are NA atoms of type A in the asymmetric unit that form primary interactions satisfying the Δ limit. At random, the expected number of these that will be to B atoms can be estimated as NASB/Stotal. Given a sample of crystal structures, the RF metric for A···B primary interactions is then defined as

data set



O N F Cl

X···H 2.7 3.0 3.5 2.2

(2.7−2.8) (2.9−3.2) (3.1−3.8) (2.0−2.4)

X···C 0.5 0.5 0.5 0.5

(0.4−0.5) (0.4−0.5) (0.4−0.6) (0.4−0.6)

X···X 0.1 0.4 0.7 0.9

(0.1−0.1) (0.3−0.5) (0.6−0.8) (0.8−1.0)

a Each RF value is followed by its 95% confidence interval (in parentheses).

four X···H interactions have RF > 2; in other words, they occur more than twice as often as would be expected from surfacearea considerations. Remarkably, the highest value (3.5) is for F···H, although the G&LP results make it clear that CH···O and CH···N are energetically stronger interactions than C−H··· F. Referring to eq 1, the observed number of F···H primary interactions, O(F···H)i, exceeds the expected number, E(F··· H)i, in all but 13 of the 115 structures in the CHF data set. RF values for X···C are all about 0.5, while those for X···X vary from 0.1 for X = O to 0.9 for X = Cl. The low value for RF(O··· O) is unsurprising since short O···O contacts are likely to be electrostatically unfavorable. The higher value for RF(Cl···Cl) may be partly due to interactions of the halogen-bonding type, when the geometry of the Cl···Cl contact enables an electronrich region of one chlorine atom to interact with the σ-hole of the other.26 ConQuest searches of the CHCl set found that 58 of the 197 structures contain Cl···Cl contacts with the appropriate geometry (Figure 1). On the other hand, we must bear in mind that the total number of Cl···Cl primary interactions is only about as many as would be expected by chance.

Figure 1. Search query for investigation of Cl···Cl contacts: d < sum of vdw radii +0.3 Å; 70 < θ1 < 110°; 160 < θ2 < 180°. B

DOI: 10.1021/acs.cgd.6b00736 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Tables 2 and 3 give RF values for primary interactions that are, respectively, shorter and longer than the sum of vdw radii.

(relative to vdw radii) of X atoms show more random behavior than do the shortest contacts. Returning to the values in Table 1, the finding that RF(F···H) exceeds both RF(N···H) and RF(O···H) is surprising and contradicts the 2014 study of RF values,16 which, as I have mentioned, was performed on a much more diverse set of structures than any of the data sets used here. A very important consideration here is that RF(F···H) is not simply governed by the energy of the F···H interaction but also by the energies of the other interactions that the fluorine atom might form. Interaction energies are usually estimated by calculating the difference between the energy of a molecule pair separated at an optimum distance and the energy of the pair separated at infinity. However, separation at infinity is not an option for a molecule in a crystal. Each atom in a crystal structure must be somewhere near an atom in another molecule, unless it is completely buried within the molecule to which it belongs, which is unlikely for a terminal atom such as fluorine. For fluorine atoms in the CHF data set, the only options are F···H, F···C, and F···F. Since the hydrogen atoms are likely to be δ+, the majority if not all of the carbon and fluorine atoms are likely to be δ-, so F···C and F···F interactions will probably be electrostatically unfavorable. Hence, there are two driving forces for packing arrangements with F···H contacts: the attractive nature of this contact and the repulsive nature of the alternatives. In crystal structures containing more chemically diverse molecules, it is possible that there are more ways in which fluorine atoms can form attractive interactions. Every structure in the CHOF data set, for example, contains at least one carbonyl group, and it has been shown that the F···CO interaction is energetically favorable.27 It is no surprise, then, that RF(F···H) in this data set is only 2.4 (95% confidence interval 2.3−2.5), much closer to the value seen in the 2014 study. The RF value for primary interactions between F and carbonyl carbon is 1.3 (1.0−1.6). It is also known that the energies of carbonyl−carbonyl interactions can be comparable with those of hydrogen bonds.28 In the CHO data set, the RF value for primary interactions between O and carbonyl carbon is 1.5 (1.3−1.6). The possibility of forming this interaction may lower the probability that oxygen atoms will form O···H primary interactions, another possible reason why RF(O···H) in Table 1 is less than RF(F···H).

Table 2. RF Values for X···H, X···C, and X···X Primary Interactions Shorter than the Sum of vdw Radii, where X = O, N, F, and Cla data set



O N F Cl

X···H 2.9 3.6 3.7 2.3

(2.8−2.9) (3.4−3.7) (3.2−4.2) (2.0−2.6)

X···C 0.4 0.3 0.5 0.5

(0.4−0.4) (0.3−0.4) (0.4−0.7) (0.4−0.6)

X···X 0.1 0.3 0.7 0.9

(0.0−0.1) (0.2−0.4) (0.5−0.8) (0.8−1.0)


Each RF value is followed by its 95% confidence interval (in parentheses).

Table 3. RF Values for X···H, X···C, and X···X Primary Interactions at or Longer than the Sum of vdw Radii, where X = O, N, F, and Cla data set



O N F Cl

X···H 2.1 1.6 3.2 2.1

(1.9−2.3) (1.3−1.8) (2.6−3.7) (1.8−2.4)

X···C 0.7 0.9 0.5 0.6

(0.6−0.8) (0.8−1.0) (0.4−0.7) (0.4−0.7)

X···X 0.2 0.7 0.7 0.9

(0.1−0.3) (0.6−0.9) (0.6−0.9) (0.8−1.0)

a Each RF value is followed by its 95% confidence interval (in parentheses).

The shorter contacts have higher RF(X···H) values than the longer interactions, especially when X = N. However, the longer contacts all have RF(X···H) significantly greater than 1, and, in the case of X = F, the lower confidence limit of RF is as high as 2.6. Therefore, the primary interactions of X atoms are nonrandomly distributed even when they are longer than the sum of vdw radii. RF values based on O···H primary interactions shorter than the sum of vdw radii were also determined for two subsets of the CHO data set, one comprising structures of molecules with ≤20 atoms and the other containing those of molecules with >20 atoms. The two RF values were, respectively, 3.0 (95% confidence interval 2.8−3.2) and 2.8 (2.8−2.9). Although the difference is in the direction anticipated from G&LP’s assertion that short C−H···O interactions are more important in small molecules, it is not statistically significant. Table 4 gives RF values based on primary, secondary, and tertiary interactions with Δ ≤ 1.0 Å. Comparison with Table 1

SO WHERE ARE WE? In crystal structures containing only C, H, and X atoms (X = O, N, F, Cl), the electronegative X atoms form many more intermolecular interactions to hydrogen atoms than would be expected from surface area considerations if packing were random. The effect is apparent both for contacts shorter than the sum of the vdw radii of the interacting atoms and for longer interactions. It is particularly marked for interactions with X = F, which are over-represented by a factor of more than 3. X···H interactions involving O, N, and Cl atoms all occur more than twice as often as would be expected by chance. The results are highly statistically significant. It really seems justified to conclude that X···H interactions, even when longer than the sum of vdw radii, are relevant in stabilizing crystal packing arrangements, including for the contentious cases when X = Cl and, especially, X = F. The reason why is less clear. The simplest explanation is that X···H interactions are sufficiently favorable in themselves to ensure their over-representation in crystal structures. However,

Table 4. RF Values for X···H, X···C, and X···X Primary, Secondary and Tertiary interactions with Δ ≤ 1 Å, where X = O, N, F, and Cla data set



O N F Cl

X···H 2.2 2.2 2.5 2.1

(2.2−2.3) (2.1−2.2) (2.4−2.7) (2.0−2.2)

X···C 0.7 0.8 0.7 0.8

(0.7−0.7) (0.8−0.8) (0.7−0.8) (0.7−0.8)

X···X 0.2 0.5 0.8 0.8

(0.1−0.2) (0.4−0.5) (0.7−0.8) (0.8−0.8)

a Each RF value is followed by its 95% confidence interval (in parentheses).

shows that the inclusion of secondary and tertiary contacts causes all but one of the RF values to move toward 1, those for X···H getting smaller and those for X···C and X···X becoming larger. Therefore, the second- and third-shortest interactions C

DOI: 10.1021/acs.cgd.6b00736 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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(9) Cotton, F. A.; Daniels, L. M.; Jordan, G. T., IV; Murillo, C. A. Chem. Commun. 1997, 1673−1674. (10) Dunitz, J. D.; Gavezzotti, A. Chem. Soc. Rev. 2009, 38, 2622− 2633. (11) Dunitz, J. D. IUCrJ 2015, 2, 157−158. (12) Thalladi, V. R.; Weiss, H.-C.; Bläser, D.; Boese, R.; Nangia, A.; Desiraju, G. R. J. Am. Chem. Soc. 1998, 120, 8702−8710. (13) Aakeröy, C. B.; Evans, T. A.; Seddon, K. R.; Pálinkó, I. New J. Chem. 1999, 23, 145−152. (14) Kryachko, E.; Scheiner, S. J. Phys. Chem. A 2004, 108, 2527− 2535. (15) Chopra, D.; Guru Row, T. N. CrystEngComm 2011, 13, 2175− 2186. (16) Taylor, R. CrystEngComm 2014, 16, 6852−6865. (17) Gavezzotti, A.; Lo Presti, L. Cryst. Growth Des. 2016, 16, 2952− 2962. (18) Groom, C. R.; Bruno, I. J.; Lightfoot, M. P.; Ward, S. C. Acta Crystallogr., Sect. B: Struct. Sci., Cryst. Eng. Mater. 2016, 72, 171−179. (19) Gavezzotti, A. J. Phys. Chem. B 2003, 107, 2344−2353. (20) Jeffrey, G. A.; Saenger, W. Hydrogen Bonding in Biological Structures; Springer: Berlin, 1991. (21) Bruno, I. J.; Cole, J. C.; Edgington, P. R.; Kessler, M.; Macrae, C. F.; McCabe, P.; Pearson, J.; Taylor, R. Acta Crystallogr., Sect. B: Struct. Sci. 2002, 58, 389−397. (22) Infantes, L.; Motherwell, S. Struct. Chem. 2004, 15, 173−184. (23) Rowland, R. S.; Taylor, R. J. Phys. Chem. 1996, 100, 7384−7391. (24) Alvarez, S. Dalton Trans. 2013, 42, 8617−8636. (25) Bondi, A. J. Phys. Chem. 1964, 68, 441−451. (26) Clark, T.; Hennemann, M.; Murray, J. S.; Politzer, P. J. Mol. Model. 2007, 13, 291−296. (27) Paulini, R.; Müller, K.; Diederich, F. Angew. Chem., Int. Ed. 2005, 44, 1788−1805. (28) Allen, F. H.; Baalham, C.; Lommerse, J. P. M.; Raithby, P. R. Acta Crystallogr., Sect. B: Struct. Sci. 1998, 54, 320−329.

the results of G&LP argue against. A slightly more complicated explanation relies on the notion that every atom must be somewhere. If an X atom in a CHX structure does not form its shortest interaction (relative to vdw radii) to an H atom, it must form it to C or X. Hydrogen atoms tend to be slightly electropositive, so, to balance this out, the C and X atoms will tend to be slightly electronegative and X···C and X···X interactions will tend to be unfavorable, increasing the tendency for X···H contacts. I have tacitly assumed throughout that if an interaction occurs significantly more often than expected by chance it, ipso facto, has a significant influence on crystal packing. Is that justified? Surely so, for what we mean by an interaction influencing crystal packing is that molecules tend to crystallize in arrangements which enable the interaction to formand this therefore results in it occurring more often than expected by chance. We have seen that X···H interactions are over-represented by factors between 2 and 3.5. How impressive is that? My 2014 study16 showed that strong hydrogen bonds (OH or NH donors and O, N or halide acceptors) and very strong halogen bonds (I···N) can be over-represented by factors of 5 to 10, so they clearly and unsurprisingly influence crystal packing much more. However, the degree of over-representation seen here for X···H interactions is comparable to those previously determined for moderate-strength halogen bonds (I···O, Br··· O, and Br···N). It took me 30 years to be persuaded that C−H···F−C and C−H···Cl−C contacts matter, but I remain of this view. Whether this belief is accepted by others or not, one thing is clear: any explanation of the crystal packing of the structures discussed herein must account for the fact that they contain many more X···H interactions than would be expected by chance.


S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.6b00736. CSD reference codes of CHOF data set (PDF)


Corresponding Author

*E-mail: [email protected]. Tel: +44 1923 775972. Notes

The author declares no competing financial interest.

■ ■

ACKNOWLEDGMENTS Colin Groom of the Cambridge Crystallographic Data Centre is thanked for helpful comments. REFERENCES

(1) Taylor, R.; Kennard, O. J. Am. Chem. Soc. 1982, 104, 5063−5070. (2) Sutor, D. J. Nature 1962, 195, 68−69. (3) Donohue, J. In Structural Chemistry and Molecular Biology; Rich, A., Davidson, N., Eds.; Freeman: San Francisco, 1968; pp 443−465. (4) Desiraju, G. R. Acc. Chem. Res. 1991, 24, 290−296. (5) Desiraju, G. R. Acc. Chem. Res. 1996, 29, 441−449. (6) Gu, Y.; Kar, T.; Scheiner, S. J. Am. Chem. Soc. 1999, 121, 9411− 9422. (7) Desiraju, G. R.; Steiner, T. The Weak Hydrogen Bond in Structural Chemistry and Biology; Oxford University Press: Oxford, 1999. (8) Bernstein, J. Cryst. Growth Des. 2013, 13, 961−964. D

DOI: 10.1021/acs.cgd.6b00736 Cryst. Growth Des. XXXX, XXX, XXX−XXX