The H-bonding outcomes in crystal structures of simple molecules,  where two potential H-bonds can be formed, have been used to  calculate relative H-bond probabilities for 59 combinations of Hbond donors and H-bond acceptors. H-bond probabilities are  shown to correlate well with the difference in solution phase free  energy between the two competing H-bonds.We acknowledge the financial support from the EPSRC through a CASE award scheme in collaboration with the Cambridge Crystallographic Data Centre.This is the author accepted manuscript. The final version is available from RSC via http://dx.doi.org/10.1039/C5CE02223

Feeder, N

Hunter, CA

McKenzie, J

CrystEngComm

The H-bonding outcomes in crystal structures of simple molecules, where two potential H-bonds can be formed, have been used to calculate relative H-bond probabilities for 59 combinations of H-bond donors and H-bond acceptors. H-bond probabilities are shown to correlate well with the difference in solution phase free energy between the two competing H-bonds

Apollo (Cambridge)

CrystEngCommCOMMUNICATIONCite this: CrystEngComm, 2016, 18,394Received 13th November 2015,Accepted 27th November 2015DOI: 10.1039/c5ce02223awww.rsc.org/crystengcommH-bond competition experiments in solution andthe solid state†‡James McKenzie,a Neil Feederb and Christopher A. Hunter*aThe H-bonding outcomes in crystal structures of simple mole-cules, where two potential H-bonds can be formed, have beenused to calculate relative H-bond probabilities for 59 combinationsof H-bond donors and H-bond acceptors. H-bond probabilitiesare shown to correlate well with the difference in solution phasefree energy between the two competing H-bonds.Analysis of intermolecular contacts in the CambridgeStructural Database (CSD) has provided importantfundamental insights into the nature of non-covalentinteractions.1–7 The structural properties of functional groupinteractions in the solid state correlate well with ab initio cal-culations of interaction potentials in the gas phase and withsolution phase spectroscopic properties, such as infraredbond stretching frequencies.8–15 Studies of intermolecularinteractions in the solid state have focussed on geometricalproperties that can be directly measured in X-ray crystal struc-tures: interatomic distances, and the relative distributions offunctional groups in three-dimensional space.16,17 However,the frequency distributions of functional group contacts inthe CSD should also provide thermodynamic informationabout relative functional group interaction energies.18,19 Inthis paper, we show that experimentally determined solutionphase H-bond parameters provide a good prediction of theprobability of functional group interactions in the CSD. Theresults imply that the frequency distribution of functionalgroup contacts in the CSD could provide a useful tool for theprediction of interaction energies in different environments.The relative stabilities of solution phase functional groupinteractions can be quantified using experimentally derivedH-bond parameters, α and β (Fig. 1(a)).20 By summing overpairwise contacts between solvent and solute, the Gibbs freeenergy of complex formation, ΔG°, can be reliably estimatedusing eqn (1).ΔG° = − (α − αS)(β − βS) + 6 kJ mol−1 (1)where α and β are the H-bond donor and acceptor parame-ters of the solutes, αS and βS are the corresponding H-bondparameters of the solvent, and 6 kJ mol−1 is the adverse freeenergy for solution-phase bimolecular association.A similar approach can be used to estimate the differencein free energy between two different H-bonded complexes insolution (Fig. 1(b), eqn (2)). This H-bond competition experi-ment provides a convenient tool for tackling the relationshipbetween solution phase and solid state interaction energies.ΔG°1 = −ΔG°2 = (α − αS)(β1 − β2) (2)where ΔG°1 and ΔG°2 are the free energy changes for the for-wards and backwards equilibrium in Fig. 1(b).394 | CrystEngComm, 2016, 18, 394–397 This journal is © The Royal Society of Chemistry 2016aDepartment of Chemistry, University of Cambridge, Lensfield Road, CambridgeCB2 1EW, UK. E-mail: herchelsmith.orgchem@ch.cam.ac.ukb The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB21EZ, UK† Electronic supplementary information (ESI) available: Conquest searchmethods, CSD data and solution phase H-bond functional group parameters.See DOI: 10.1039/c5ce02223aFig. 1 (a) Formation of a H-bonded complex between two solutes insolution is determined by the equilibrium between solute–solventinteractions in the free state and solute–solute (A·D) and solvent–sol-vent (S·S) interactions in the bound state. (b) Competition between twodifferent H-bond acceptors (A1 and A2) for one H-bond donor (D) insolution. The energy of each pairwise interaction can be estimated asthe product of the relevant H-bond parameters.Open Access Article. Published on 21 December 2015. Downloaded on 10/11/2017 14:52:17.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article OnlineView Journal  | View IssueCrystEngComm, 2016, 18, 394–397 | 395This journal is © The Royal Society of Chemistry 2016Eqn (2) and the frequency distribution of functional groupinteractions in the CSD can be used to compare the competi-tion between two different H-bonding interactions in solutionwith the outcome of the competition between the same twointeractions in the solid state. If we select molecules that con-tain one H-bond donor (D), two different H-bond acceptors(A1 and A2) and hydrocarbon only, then two differentH-bonded states are possible in the solid state (Fig. 2). If suf-ficient X-ray crystal structure data are available for reliablestatistics, the populations of the two different H-bondedstates in the solid state should be related to the solutionphase free energy for the competition equilibrium in a hydro-carbon solvent (Fig. 1(b)).We therefore searched the CSD21 for molecules that con-tain only two functional groups, one of which is both aH-bond donor and a H-bond acceptor, and the other is only aH-bond acceptor. The frequency of occurrence of the two dif-ferent H-bonds in the CSD was used to calculate the probabil-ity of H-bond formation in the solid state, pi (eqn (3)).(3)where Ni are the number of structures in the CSD whichcontain both functional groups as the only non-hydrocarbonfunctionality and where the H-bond of interest is formed(i = 1 or 2 for the D·A1 or D·A2 interaction respectively).The error in pi, εi, is given by eqn (4). For some systems,pi values of 1 and 0 were obtained, because one of the twoH-bonds was never observed. For these systems, the error inpi cannot be estimated.(4)Table 1 lists the functional groups studied in the H-bondcompetition experiments reported in this work. For each pairof functional groups in Table 1, the CSD was searched usinga formula constraint to ensure that one of each functionalgroup was present in the molecule with only a variable hydro-carbon skeleton connecting them. The criterion used todetect a H-bond was any contact between the specified atomsthat was closer than the sum of the van der Waals radii, andthe number of structures containing D·A1 and D·A2 H-bondswas recorded (see ESI†).For certain functional group combinations the same crys-tal structure was retrieved in searches for D·A1 and for D·A2,i.e. the crystal contained both possible H-bonds. These struc-tures were checked manually for artefacts. For example,Fig. 3 shows two results where both interactions were foundin the competition experiment between a ketone acceptorand an alcohol acceptor for an alcohol donor. In Fig. 3(a),the presence of two ketone–alcohol H-bonds (O1A·O2B andO1B·O2A) forces the alcohol oxygens (O1A and O2A) intoclose proximity, so that the interatomic distance is shorterthan the sum of the van der Waals radii. There is no hydro-gen atom between O1A and O2A, so this H-bond wasremoved as a hit from the search. In contrast Fig. 3(b) showsthat in a different structure both ketone–alcohol (O3B·O2A)and alcohol–alcohol (O1A·O2A) H-bonds are present.The values of pi calculated from the CSD data can be com-pared with the free energy change for the corresponding solu-tion phase competition experiment, ΔG°i . The values of solu-tion phase H-bond parameters for a specific functional groupvary with substituent (see ESI†). We therefore used a data-base of experimentally derived H-bond parameters to obtaingeneric values of α and β for each functional group, andthese values were used in eqn (2) to calculate the free energychange for the solution phase H-bond competition experi-ment in a hydrocarbon solvent.22 The α value for the solventwas chosen as 0.7 (the average value of α for an aliphatic CHand an aromatic CH, which are 0.4 and 1.0 respectively). Theresults are not very sensitive to the precise value used asFig. 2 Competition of two different H-bond acceptors (A1 and A2) forone H-bond donor (D) in the solid state. The difference in the stabilitiesof the two different H-bonds determines the probability of formationof one of the two states.Table 1 Functional groups studied and the corresponding solution phaseH-bond parameters, α and β22Functional groups α βAlcohol 2.7 5.3Phenol 3.6 3.0Secondary alkyl amide 2.9 8.1Secondary alkyl aniline 2.1 4.4Secondary sulphonamide 3.1 5.9Pyrrole 3.0 3.9Carboxylic acid 3.6 4.9Ketone 5.8Nitrile 5.0Alkyl ether 5.5Aryl ether 3.1Ester 5.4Tertiary sulphonamide 6.0Sulphone 6.2Tertiary amine 7.8Sulphoxide 8.6Trialkyl phosphine oxide 10.7Pyridine 7.4N,N-Dialkyl carbamate 7.2N,N-Diaryl carbamate 6.1Nitroalkane 3.8N,N-Dialkyl aniline 4.6CrystEngComm CommunicationOpen Access Article. Published on 21 December 2015. Downloaded on 10/11/2017 14:52:17.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Online396 | CrystEngComm, 2016, 18, 394–397 This journal is © The Royal Society of Chemistry 2016hydrocarbon is a very weak competitor for H-bonds. Theresults are compared with the corresponding H-bond fre-quency distribution in the solid state in Fig. 4. The 59 differ-ent functional group combinations studied produce 118 datapoints in Fig. 4, because each competition experiment givestwo results, p1 and p2.Although there is considerable scatter in Fig. 4, there is aclear correlation between the solution phase ΔG°i values andsolid state pi values. If the frequency distribution of solidstate H-bond interactions were determined by the solutionphase free energy change for the competition experiment,then we would expect a Boltzmann distribution according toeqn (5). Eqn (5) is represented by the red line in Fig. 4.(5)The root mean square error between the theoretical lineand the experimental data in Fig. 4 is large (RMSE = 0.20).One of the outliers in Fig. 4 is the competition of an alcoholH-bond for an alcohol H-bond acceptor and an aryl etherH-bond acceptor. The alcohol–alcohol H-bond is 3 kJ mol−1more stable that the alcohol-aryl ether H-bond according tothe solution phase H-bond parameters, but the populationsof these H-bonds in the CSD are equal (52% and 48% respec-tively, see ESI†). Fig. 5 illustrates some of the structures inthe CSD that give rise to this behaviour. Of the 22 structuresthat contain an alcohol-aryl ether H-bond 9 have the genericstructure shown in Fig. 5(a). In these structures, the C–OHbond is coplanar with the aromatic ring, which stericallyblocks H-bond donors from interacting with the alcohol lonepairs. Fig. 5(b) shows another example where a rigid polycy-clic ring structure sterically blocks the alcohol group fromacting as a H-bond acceptor. This outlier in Fig. 4 is thereforedue to a small number of structures with particular stericproperties. This is a general problem with functional groupcombinations that yielded a relatively small number of hitsin the CSD search.The issue of poor sampling can be addressed by combin-ing data from different searches. Fig. 4 compares the numberof H-bonds observed in the CSD with solution phase H-bondfree energy differences for specific functional group combina-tions. However, some functional group combinations havevery similar values of ΔG°i . It is therefore possible to pool theCSD data from different searches by combining the resultsfor solid state H-bond competition experiments with similarsolution phase values of ΔG°i . The values of pi were thereforerecalculated by summing the values of Ni for all systemswhere the values of ΔG°i fall within a 2 kJ mol−1 window. Theresults are shown in Fig. 6. The agreement between the fre-quency distribution of H-bonding interactions in the solidFig. 3 X-ray crystal structures containing both D·A1 and D·A2 closecontacts. (a) In KEFYOJ, the formation of H-bonds between O1A andO2B and between O1B and O2A forces O1A and O2A into close con-tact, but this is not a H-bond. (b) In CAZXAC10, close contactsbetween O1A and O2A and between O2A and O3B are observed andboth are H-bonds.Fig. 4 Relationship between ΔG°i and pi for all functional groupcombinations in Table 1 (RMSE = 0.20). The red line corresponds tothe Boltzmann distribution in eqn (5).Fig. 5 The solid state H-bond competition of an alcohol H-bonddonor for an alcohol H-bond acceptor and an aryl ether H-bondacceptor is affected by steric crowding (shown in blue). a) A structuralfamily of 9 compounds where steric effects prevent the alcohol fromacting as a H-bond acceptor (X = Me or H, R = alkyl or aryl, ref codes:SECWIG, MXMCHX, MOVXAX, MOVWIE, FOPWIR, FOPWEN, DECBUK,DECBOE, COMJET). b) A rigid polycyclic ring structure blocks the alco-hol lone pairs (ref code: RUXLUR).CrystEngCommCommunicationOpen Access Article. Published on 21 December 2015. Downloaded on 10/11/2017 14:52:17.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article OnlineCrystEngComm, 2016, 18, 394–397 | 397This journal is © The Royal Society of Chemistry 2016state and solution phase H-bond free energies is significantlybetter than obtained for the raw data in Fig. 4.These results indicate that the solution phase H-bondparameters α and β provide an accurate indicator of the prob-ability of forming a H-bonding interaction in the solid state.This observation is consistent with the success of cocrystalscreening approaches based on this assumption.23–25 Theresults also suggest that the CSD could provide a valuableresource for quantifying the relative strengths of inter-molecular functional group interactions. The frequency distri-butions of functional group contacts in the CSD are directlyrelated to the corresponding interaction energies in solutionand may ultimately be useful for calibration of intermolecularpotentials for use in molecular modelling applications.AcknowledgementsWe acknowledge the financial support from the EPSRCthough a CASE award scheme in collaboration with the Cam-bridge Crystallographic Data Centre.Notes and references1 J. Kroon and J. A. Kanters, Nature, 1974, 248, 667.2 P. Murray-Rust and W. D. S. Motherwell, J. Am. Chem. Soc.,1979, 101, 4374.3 R. Taylor and O. Kennard, J. Am. Chem. Soc., 1982, 104, 5063.4 F. H. Allen, C. A. Baalham, J. P. M. Lommerse and P. P.Raithby, Acta Crystallogr., Sect. B: Struct. Sci., 1998, 54, 320.5 R. Taylor, Acta Crystallogr., Sect. D: Biol. Crystallogr.,2002, 58, 879.6 F. H. Allen and W. D. S. Motherwell, Acta Crystallogr., Sect.B: Struct. Sci., 2002, 58, 407.7 F. H. Allen and R. Taylor, Chem. Soc. Rev., 2004, 33, 463.8 S. L. Price and A. J. Stone, Mol. Phys., 1982, 47, 1457.9 S. L. Price, A. J. Stone, J. Lucas, R. S. Rowland and A. E.Thornley, J. Am. Chem. Soc., 1994, 116, 4910.10 J. P. M. Lommerse, A. J. Stone, R. Taylor and F. H. Allen,J. Am. Chem. Soc., 1996, 118, 3108.11 F. H. Allen, C. A. Baalham, J. P. M. Lommerse, P. R. Raithbyand E. Sparr, Acta Crystallogr., Sect. B: Struct. Sci., 1997, 53,1017.12 J. P. M. Lommerse, S. L. Price and R. Taylor, J. Comput.Chem., 1997, 18, 757.13 I. Nobeli, S. L. Price, J. P. M. Lommerse and R. Taylor,J. Comput. Chem., 1997, 18, 2060.14 F. H. Allen, C. A. Baalham, J. P. M. Lommerse and P. R.Raithby, Acta Crystallogr., Sect. B: Struct. Sci., 1998, 54, 320.15 A. Novak, Struct. Bonding, 1974, 18, 177.16 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G.Orpen and R. Taylor, J. Chem. Soc., Perkin Trans. 2,1987, S1–S19.17 T. Steiner, Angew. Chem., Int. Ed., 2002, 41, 48.18 S. Miyazawa and R. L. Jernigan, Macromolecules, 1985, 18,534.19 M. J. Sippl, J. Mol. Biol., 1990, 213, 859.20 C. A. Hunter, Angew. Chem., Int. Ed., 2004, 43, 5310.21 F. H. Allen, Acta Crystallogr., Sect. B: Struct. Sci., 2002, 58,380.22 C. S. Calero, J. Farwer, E. J. Gardiner, C. A. Hunter, M.Mackey, S. Scuderi, S. Thompson and J. G. Vinter, Phys.Chem. Chem. Phys., 2013, 15, 18262.23 D. Musumeci, C. A. Hunter, R. Prohens, S. Scuderi and J. F.McCabe, Chem. Sci., 2011, 2, 883.24 T. Grecu, C. A. Hunter, E. J. Gardiner and J. F. McCabe,Cryst. Growth Des., 2014, 14, 165.25 T. Grecu, H. Adams, C. A. Hunter, J. F. McCabe, A. Portelland R. Prohens, Cryst. Growth Des., 2014, 14, 1749.Fig. 6 Relationship between ΔG°i and pi obtained by summing H-bondpopulations over 2 kJ mol−1 windows in ΔG°i (RMSE = 0.07). The redline corresponds to the Boltzmann distribution in eqn (5).‡ Data Access. All data supporting this study are provided as supplementary in-formation accompanying this paper.CrystEngComm CommunicationOpen Access Article. Published on 21 December 2015. 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H-bond competition experiments in solution and the solid state

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