J . Am. Chem. SOC. 1982, 104, 5063-5070
5063
Crystallographic Evidence for the Existence of C-H-0, C-H-N, and C-,H.-Cl Hydrogen Bonds Robin Taylor* and Olga Kennard' Contribution from the Crystallographic Data Centre, University Chemical Laboratory, Cambridge CB2 1E W, England. Received December 21, I981
Abstract: A survey of 113 published neutron diffraction crystal structures is described. The major results are as follows. Hydrogen atoms that are covalently bonded to carbon have a statistically significant tendency to form short intermolecular contacts to oxygen atoms rather than to carbon or hydrogen atoms. This phenomenon is probably due to electrostatic stabilization of the short C-H.-0 contacts. The proton in the majority of short C-H-0 contacts lies within 30' of the plane containing the lone-pair orbitals of the oxygen atom. C-H groups that are adjacent to nitrogen atoms are particularly likely to participate in short C-H-0 interactions, but the environment of the oxygen atom is unimportant. The crystal structures also contain several short, intermolecular C-H-N and C-H-CI contacts. It is concluded that the C-H-0, C-H-N, and C-H.-CI interactions are more likely to be attractive than repulsive and can reasonably be described as hydrogen bonds. The ability of carbon atoms to act as proton donors in hydrogen bonds has been the subject of controversy for many years. Spectroscopic studies24 indicate that C-H-X hydrogen bonds occur in many systems, a conclusion that is supported by quantum mechanicals8 and empirical potential energy calculation^.^ (The symbol X is used throughout the text to denote a hydrogen bond acceptor atom, i.e., 0, N, C1, or S). However, the crystallographic evidence for C-Ha-X hydrogen bonding is sparse and circumstantial. A survey of crystal structures containing short C-H.-0 contacts was conducted by Sutor in 1963.1° She concluded that the short contacts could best be described as hydrogen bonds, but this interpretation was later challenged by Donohue." In the last 10 years, C-H-X (especially C-H--0) hydrogen bonds have been postulated in many crystal structures, particularly those of nucleosides12and amino acids.13 However, to the best of our knowledge, no further systematic survey of the crystallographic data has been carried out. We have therefore conducted such a survey, with a view to answering the following questions: (1) What crystallographic evidence is there for the existence of CH.-X hydrogen bonds? (2) In what types of crystal structures are they likely to occur? Crystallographic Data The crystallographic data used in the survey were retrieved from the Cambridge Structural D a t a b a ~ e . ' ~A total of 113 organic crystal structures were used (Table I). They contain 661 crystallographically independent (C-)H atoms (the symbol (C-)H is used throughout the text to denote a hydrogen atom that is covalently bonded to carbon). The criteria used to select the structures were as follows: (1) All of the structures were determined by neutron diffraction, since the survey depends on an accurate knowledge of the (C-)H atomic positions. (2) Each structure contains at least one (C-)H atom and at least one (1) External staff, Medical Research Council. (2) Green, R. D. "Hydrogen Bonding by C-H groups"; Wiley Interscience: New York, 1974. (3) Ts'o, P. 0. P.; Kondo, N. S.; Schweizer, M. P.; Hollis, D. P. Biochemistry 1969, 8, 997-1029. (4) Harmon, K. M.; Gennick, I.; Madeira, S. L. J . Phys. Chem. 1974,78, 2585-2591. (5) Kollman, P.; McKelvey, J.; Johansson, A.; Rothenberg, S. J . Am. Chem. SOC.1975, 97, 955-965. (6) Umeyama, H.; Morokuma, K. J . Am. Chem. SOC. 1977, 99, 1316- 1332. (7) Vishveshwara, S. Chem. Phys. Left. 1978, 59, 26-29. (8) Gay, R.; Vanderkooi, G. J. Chem. Phys. 1981, 75, 2281-2289. (9) Leiserowitz, L., private communication. (10) Sutor, D. J . J . Chem. SOC.1963, 1105-1110. (1 1 ) Donohue, J. In "Structural Chemistry and Molecular Biology"; Rich, A., Davidson, N., Eds.; W. H. Freeman: San Francisco, 1968; pp 459-463. (12) Saenger, W. Angew. Chem. Znf. Ed. Engl. 1973, 12, 591-601. (13) Jeffrey, G. A.; Maluszynska, H. Znf. J . Bioi. Macromol. 1982, 4, 173-185. (14) Allen, F. H.; Bellard, S.; Brice, M. D.; Cartwright, B. A.; Doubleday, A.; Higgs, H.; Hummelink, T.;Hummelink-Peters, B. G.; Kennard, 0.; Motherwell, W. D. S.;Rodgers, J. R.; Watson, D. G. Acta Crystallogr., Sect. 8 1979,835, 2331-2339.
0002-7863/82/1504-5063$01.25/0
potential hydrogen bond acceptor atom (0, N, Cl, S). (3) Structures with R factors greater than 0.10, or which were determined from very limited data, or which exhibit disorder, were excluded. (4) Structures which were determined at low temperatures, or which contain deuterated species, were included in the survey. Both factors might have a slight effect on the observed (C-)H atom geometrie~.'~However, the number of structures involved is small (about 15% of the total sample), and they were considered to be of sufficient chemical interest to warrant their inclusion.
Crystallographic Evidence for the Existence of C-Ha-0 Hydrogen Bonds We consider first the crystallographic evidence for the C-H-0 hydrogen bond. C-H.-N, C-H-Cl, and C-H-.S interactions are discussed in the following section. Nearest-Neighbor Contacts of (C-)H Atoms. The most important geometrical characteristic of hydrogen bonds is that the distance between the proton and the acceptor atom is shorter than the sum of their van der Waals radii.I6 We therefore began our investigation by calculating the "nearest-neighbor contact" of each (C-)H atom in the sample. The "nearest-neighbor contact", (C-)H-Y, is defined here as the shortest contact formed by the (C-)H atom, relative to the sum of the corresponding van der Waals radii, Le., the contact for which the value of d in the following equation is a maximum: d = v(H) u(Y) - r(H-Y) (1)
+
(u(H) = van der Waals radius of (C-)H; u(Y) = van der Waals radius of Y ;r(H.-Y) = (C-)H.-Y interatomic distance). Only intermolecular contacts were considered at this stage, because short intramolecular interactions may sometimes be due to geometrical constraints within the molecule. Contacts with C-H--Y angles of less than 90° were ignored, as it is generally accepted that the donor-proton-acceptor angle in a hydrogen bond must be at least 90°. The van der Waals radii used were as follows: C = 1.75, H = 1.20," Br = 1.85, C1 = 1.75, N = 1.55, 0 = 1.50, P = 1.80, S = 1.80 A. They are based on the values given by BondiI8 and Kitaigor~dsky.'~In view of the difficulty of assigning reliable van der Waals radii to metal ions,'* contacts to Li', Na', K+, Rb+, Ca2+, and Ba2+ were ignored. (15) Takusagawa, F.; Koetzle, T.F. Acta Crystallogr., Sect. 8 1979,835, 2126-21 35. (!6) .Hamilton, W. C.; Ibers, J. A. "Hydrogen Bonding in Solids"; W. A. Benjamin: New York, 1968. (17) One of the referees has pointed out that Baur (Baur, W. H. Acta Crystallogr., Sect. B 1972, 828, 1456-1465) gives a value of 1.0 A for the van der Waals radius of hydrogen. However, this value was derived for hydrogen atoms that are covalently bonded to electronegative elements such as oxygen. Molecular mechanics calculation^^^ suggest that a larger radius should be used for (C-)H atoms that for (0-)H or (N-)H atoms. (18) Bondi, A. J. Phys. Chem. 1964, 68,441-451. (19) Kitaigorodsky, A. I. "Molecular Crystals and Molecules"; Academic Press: London. 1973. 0 1982 American Chemical Societv
Taylor and Kennard
5064 J . Am. Chem. SOC.,Vol. 104, No. 19, 1982 Table I. Bibliography
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M.0.BargOuth,G.W~l1,Cryst.Struct.Comm.,9.605,1980. lMCPROPOi1 7b 3-Merc.pt~-l.3-diphenylprop-2-en-l-one 17 Calcium m a l o n a t e dihydrate (CAnALD03I L.F.Pa~er,K.E.Turner,F.H.Moore,J.Chem.Soc..Perkln 2,249,1976. J . A l b e r t s s o n , A , O ~ k ~ ~ ~ ~ ~ ~ , CCryst.,834.2131,1978. , s ~ ~ ~ ~ ~ ~ ~ , A c t ~ 15 Methyl b e t a - D - r l b ~ p y r a n o s i d e (MDRIBP021 18 2 . 5 - D ~ c h l ~ ~ o b e n 2 e n e s u l f o n lacid c trlhydrate ICBZSULOlI V.J.James,J.D.Stevens,F.H.Uaore.A=t~ Cryst.,034.188,1918. J.ROl~e~elJ.M.W~111.mp.J.Chem.Pnvs..68.2896.19l8. 16 9-nethvl-adenine (MEADENOiI 19 Cyclodecane-1.6-trane-dial ICDECbL111 ~ . ~ . u ~ ~ ~ i i ~ n , ~ . ~ e n c ~ , ~ . ncryst.,~36.142(.1980. . c ~ ~ ~ e n , ~ c t a O . E r m e r . S . D . D u n ~ t r , l . 0 e r n ~ l , A c t ~Cryst.,B29,2218,1913. 11 Melampodin IMELAMP111 2 0 N - 1 2 - C h l o r a e t h v l i - D - ~ l u c a n a m i d e lCEGLCAO11 S.F.W~tk~~~.N.H.F~~~h~~.I.Bernal.Proc.Nat.Acad.SC~.U.S.A.,1~,2b34, A . C . S i n d t . U . F . i a c h a y ~ A ~ t ~Cryst.,B33.2659,1911. 1913. 21 Chloral hydrate ICHORLHOlI 78 M e t h y l - D - m a n n 0 p y ~ ~ n O s l d eIMEMANP111 G.U.B~0~~,H.A.L~~y,C~y~t.St~~~t.Comm..2.107,1913. ~ . ~ . ~ ~ f f ~ ~ y . ~ . ~ . n ~ n ~ ~ l cryst.,833,1i8.1911. ~ ~ , s . ~ ~ k ~ g ~ , ~ c t a 22 L-Cysteic acid monohydrate ICYSTACOlI 19 1-Methylthymine I U E T H Y M O l ~ U . R ~ m a n a d h ~ m , S . K . S I k k ~ , R . C h ~ d ~ ~ Cryst.,829,1161,1913. b~~~~,A~t~ A.K~~Ck,T.F.KO~t~l~,R.ThomaOlJ.Chem.PhyS.,61,2111.1914. 23 L-Cystine dlhydrochloride (CYSTCL021 80 N,N-Dimethyl-nltramlne IUETNAMOlI ~ . ~ . ~ ~ n e ~ , ~ . ~ e r n a ~ , n . ~ . ~ r e y c,r ~y s.t .~ ,.~ 3~~~, 1~2 t2 0~, 1~ 9~l b,. ~ c t a A.FllholIG.Bravic,M.Rey-L~fon.ll.Thom.8.Acta Cryst.,836,575.1980. 24 Cytosine monohydrate ( C Y T O S H ) 8 1 Uethyl d l p h ~ - D - g d l ~ C t 0 p y ~ . n ~ ~ ,monohydrate d~ IUGALPYOll H . P . u e b e r , 8 . n . c r a v e n , ~ . ~ . n c n u I l a n . 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C.Stalhandlke,ACtd Cryst.,B32,2806,1916. 3 3 Di-t-butylphobphinic acid IDTBUPAOII A.H.ReiS J u n i o ~ , S . W . P e t e r a o n . M . E . D r u y a n , E . G ~ b ~ ~ t , G . W . l l a s o n , D . F . P ~ p p ~ ~ d , 89 Perdeutero-formlc acld IPDEFDROl) A . A l b ~ n a t l . K . D . R o u s e , M . W . T h o m ~ ~ , A ~ tCryst.,B34,2188,1978. ~ Inorg.Chen.,15.2748,1916. 90 L-Phenylalanine hydrochloride IPHAL8COll 34 E t h y l e n e d l a m a n l u n D-tartrate IEDATAROII A . R . A l - K ~ ~ ~ g h o u i i , T . F . K a e t ~ l e , A i c tCryst.,B31.2461,1915. a C.K.Fair.E.O.Schle.eer.bcta Cryst..833,1331,1911. 91 Putrescine diphosphate lPUTRDP11) 3 5 b e t ~ - D - F ~ U C t O p y i ~lFRUCTOO2I n~~~ F . T ~ k Y 5 ~ g a u . , T . F . K O e t ~ l ~ , A C t a Cryst.,B35,861,1919. S . T ~ k ~ g ~ , G . A . J = f f ~ ~ yCry~t.,833,3510,1971. ,A~t~ de 9 2 P y ~ i d i n i Y ~ - l - d i c y ~ n o m e L h y l l lPYRCYU02I 36 Glycylglycine hydrochloride monohydrate IGLCICHOI) L . D e V O B , F . B ~ C l t , R . F O " ~ ~ t , U . T h ~ ~ ~ ~ ,C A~ Y~ btta. , B 3 6 , 1 8 0 7 , 1 9 8 0 . T . F . K O e t l l e , W . C . H ~ m i l t ~ ~ , R . P ~ ~ t h ~ ~ ~ ~Cryst.,828,2083.1912. ~thy,A~t~ 93 PyridoiinLum chloride ( P Y R X C L O I ] 31 G l v c ~ l l i c acid lGLICAClO1 G.E.Bacon,J.S.Plant,Act. Cryst..B36,1130,1980. R . D . E l l l 8 0 n . C . K . J ~ h ~ ~ ~ ~ , H . A . L e Y y , A c t a Cryat.,821.333,1911. 9 4 Pyrarolc lPYRZOL021 38 alpha-D-Glucose IGLUCSAOlI G . U . B ~ O ~ ~ , H . A . L ~ V ~ Cryst.,035,656,1919. ,A=~~ F . K . L d r 6 e n , U . S . L ~ h m ~ ~ " , I . S ~ t ~ f t e , S . E . R a ~ ~ ~ a Chem.Scand.,24, ~~~,A~t~ 3248.19io. 39 L - G l u t a m m e lGLUTAUO1) 95 Quinolinic acid lPUlCNLO2l T.P.Xoet~le,n.N.F~ey,n.s.Lehmann,Y.C.Hamllt~~,A~t~ Cryst.,B29,2511, F.T.kUI.I.Y~,T.F.Ko~t~l~,A~t= Cryst..B34.1149,1918. 1913. 96 Rubidium hydrogen Oxydiacetate IRBHOXYOlI 40 G l y c i n e IGLYCIN03I J.Alberts5on.I.Grenthe.Acta Cryst.,829,2151,1913. P . - G . J o n s B ~ n , b . K ~ ~ c k , A Cryst.,B28.1821.1912. ~t~ 9 7 Resorcinol lRESOPAl3I 41 G l y c i n e lGLYClN161 ~.~.8.c~n,~.~.~ude.z.~~i~t.,138.19,1913. A.KV~ck.Y.M.Canning,T.F.Koet.le.G.J.B.W111rams,Acta Cryst.,B36,115, 98 a l p h a - L - R h a m O s e monohydrate IRHAUAH121 1980. 42 Glycylglycine IGLYGLYOII S.Tak.gl,G.A.Jeffrey,Act. C~yat.,B34,2552,1978. 99 Salicylic acid ISALIAC12) A.KVICk,A.R.Al-K.T.qh~"l,,T,F.K~et~le,A~t~ Cryst..B33,3196.1971. G.E.~acon.R.J.Jude,Z.Kr~~t.,138.19,1913. 43 Glycine hYdrochlorIde iGLYHCLl 100 0-sulfobenroic acid trihydrate lSLBZACOll A..i.Al-Kaiaghouli .F.E.C~le,n~S.Lehmann,C.F.u~skell,J.J.verbist, R.~tt~g,J.n.mI~li.mi,x"~~g.ch~~.,i5,~051.1916. T.F.Koetile,J.Chem.Phys.,63,1360.1915. 101 S Y C C O S ~lSUCROSO41 44 6 - H y d ~ O ~ y - l - f ~ l ~ e n e c d r b a i d e h IHFULCAOlI yde G . U . B ~ O Y ~ . H . A . L ~ V ~ , A Cryst.,B29,190,1913. =~~ n.Fueea.H.J.L~ndner,Chem.Ber.,108.3096.1915. 102 1.3.5-Tri~cctylbenrene ( T A C B E N O l ) 4 5 Hippuric acid IHIPPACO2) 8.H.D'Connor.P.H.Uoore.Acta C~yst.,829,1903,1913. II.CUttle,A.L.Uacdonald,J.Chem.Soc.,Pelkln 2,181,1914. 103 Tetra-acetylethane ITACETI01 I 46 L-Hietfdlne hydrochloride monohydrate IHISTCIIllI ~ . ~ . ~ ~ ~ ~ r . ~ . ~ . ~ ~ ~ ~ ~ ~ , ~ . ~ . ~ ~ ~ ~ ~ . ~ . ~ ~ y a t . ~ o ~ . s t ~ ~ ~ t . . 5 , H.FUe6I.D.HOhlYeln.S.A.M~~~".A~t~ Crvst..833.654.1911. 1 0 4 D-TartarlC acid ITARTACOlI 4 7 4 - H y d r o x y - L - p r o l m e (HOPROL121 Y . O k a y ~ , N . R . S t e ~ p l e , U . I . K . y , A c t ~ Cryst.,21,231,1966. T.P.KOetlle,U.S.Lehm~"",W.C.HamlltO~,Acta Cryst..B29.231,1973. 105 9-Thiabicyclol3.3.1Inonrne-2.6-dionc ITBCNODOlI 4 8 Imidazole lIuAZOLl3l U.J.B~~~~~,P.J.COX,H.P.F~~~~~~,~.H,P.G~~,A.D.U.H~~~~~P.H.U~C~~~, 8.U.C1~~en,R.K.llcUlullan.J.D.B~ll,H.C.Freenan,Acta Cryst..B33,2585,1911. U . A . l l ~ c d 0 n ~ l d , G . A . S i ~ , D . N . J , W h ~ t ~ , ACryst.,B35,669.1919. ~t4 4 9 Iminodiacetic acid hydrobromide lIMDACB11I 106 1,7,8,8-Tetracyanoqu1nodin~th.ne-deutero-p-trrpheny1 Complex ITCQDTP101 A1.0skar8110n,ACta CIYat..B32.2163,1976. G . C . L i a c n ~ k y . C . K . J o h n ~ ~ n , H . A . L e v y , A C t ~ CrySt..832.2188,1916. 50 ImIdazolium hydrogei maleate lIMZMAL11l 101 T r i g l y c i n c sulfate (TGLYSUllI 8.H~u.E.O.Schlempel.bct~ Cryst..B36.3011,1980. U.I.K~y.R.Klelnbc~g,Fe~~~~l~~t~~~~,5,45,1913. 51 POtaSSlUm hydrogen axydiacetate (KAOXYAOlI 108 1.3.5-Trlnitrobcnrene lTNBENZ10) J.Albe~t.IO",I.G~enthe.hct. C~y~t.,B29,2151.1913. C.S.Choi,J.E.Abel,Acta Cry~t.,B28.193,1912. 5 2 P o t a s a i m D-gluconate monohydrate IKDGLUUOlI 109 p-Toluenesulfonlc acid monohydrate lTOLSAU121 ~.~.~.n.qiotopo~lo.,~.~.~effrey.s.~.~a~ l l l ~ a , ~ . c . ~ . m i l t o n , A c Cryet., ta J . ~ . L ~ n d g ~ e n , J . U . W I l l i~~~,J.Chen.Phy~.,58,188,1913. 830.14zi.i9id .~ .~ . 110 I-Triazine lTRIZlN02) 53 POta.siUm D-gluconate monohydrate iKDGLUMO2) ~.coppenn,scienc~,i~a,i~i7,i~6i. N.C.P~n~giotopoule.,G.A.J~ff~~y,S.J.La P l ~ ~ d , W . C . H d m i l t ~ n , A ~ tCryst.. . 111 L-Valine hydrochloride lVALEHCllI B30,1421,t914. T.~.Ko~t~lC,L.GOliC,M,S,L~h~~~~.J.J.VecbIst,Y.C.H~mlltan,J.Ch~8.PhY~.~ 54 Potassium hydrogen dicrotonate IKHCROTOlI 60,4690.1974. D . R . n c G ~ c g ~ ~ , J . C . S p ~ . L m . n , l . S . L e h m . n n . J . C h ~ ~ . S ~ ~ . , P ~ ~2,1140.1911. ki~ 111 U e t h y l bet.-D-xylopyr.no.idc lXYLO~UOl1 5 5 P0taSSIU.m hydrogen b i 8 1 1 c e t y l ~ a l i c y l a t e i IKHDASLOlI S.TaL.gi,G.A.JCfl~ey,A~t~ C ~ y ~ t . . 8 3 3 . 3 0 3 3 , 1 9 1 7 . A.SeqUeir~,C.~.B~~kebile.W.C.Hanilron,~.uoi.st~~~t.,1,283.1968. 113 alpha-L-Xy1opyrmo.c IXYLOSEOlI 5 6 P o t a s e I U n hydrogen b i s I d i ~ h l ~ i ~ t , ~ e t aIKHDCAClOI t~l S.T.k.gi,C.A.J.ff~ey,A~t~ Cry.t.,835.1482,1979. 3 Acetamide
___.-_ -.
....................................................................... T h e CambCidg.
The results are summarized in Figure 1, which shows the distribution of d for all 661 nearest-neighbor contacts (the symbol d is used throughout the teJt to denote the parameter defined in eq 1). The mean value ( d = 0.030 A) is close to zero, which
Structural Database reference c o d e IS q1V.n
In
suggests that the van der Waals radii given above are reasonably accurate. There are 46 nearest-neighbor contacts with d > 0.3 A, Le., appreciably shorter than the sum of the van der Waals radii. However, before concluding that these contacts are hydrogen
J . Am. Chem. Soc.. Vol. 104, No. 19, 1982 5065
Crystallographic Evidence for Hydrogen Bonds
8 CISTFNZE rRSGMETES
ULPHU
Figure 1. Distribution of the distance parameter d (eq 1; units are angstroms) for the (C-)H atom nearest-neighborcontacts. Three contacts with d < -0.65 A are omitted.
Table 11. Atom Types Involved in (C-)H Atom Nearest-Neighbor Contactsa obsd distbnC atom predicted contacts with contacts with type distbnb all contacts d > 0.0 A d > 0.3 A 0.04 (2) 0.16 (63) C 0.30 0.18 (122) 0.23 (90) 0.02 (1) H 0.47 0.30 (197) Br c1 N 0
0.00
P S total
0.00 0.00
0.01 0.04 0.18 1.00
0.00 ( 0 ) 0.05 (31)
0.03 (18) 0.44 (289) 0.00 ( 0 )
0.01 (4) 1.00 (661)
0.00 (0)
0.03 (13) 0.03 (11) 0.54 (211) 0.00 ( 0 ) 0.00 (1) 1.00 1389)
0.00 ( 0 ) 0.02 (1) 0.00 ( 0 )
0.91 (42)
ai
(eq 3; oxygen van der Waals radius = 1.50
A). Table 111. Atom Types Involved in (C-)H Atom Nearest-NeighborContactsa obsd distbn‘ atom predicted contacts with contacts with tvue distbnb all contacts d > 0.0 A d > 0.3 A C 0.30 0.21 (136) 0.20 (67) 0.11 (2) H 0.47 0.35 (233) 0.30 (100) 0.05 (1) Br C1
0.00 0.01
0.00 ( 0 ) 0.05 (31)
0.00 ( 0 )
0.00 ( 0 )
0.03 (18) 0.36 (239)
0.04 (13) 0.03 (11) 0.43 (145)
N 0 P S
0.04 0.18 0.00
0.00 ( 0 )
0.00 ( 0 )
0.05 (1) 0.00 (0) 0.79 (15) 0.00 ( 0 ) 0.00 (0)
0.01 (4) 0.00 (1) total 1.00 1.00 (661) 1.00 (337) 1.00 (19) a Results obtained with an oxygen van der Waals radius of 1.40 A. Normalized to unity. Normalized to unity. Figures in parentheses are the actual numbers of contacts observed.
0.00 ( 0 ) 0.00 ( 0 )
1.00 (46)
Results obtained with an oxygen van der Waals radius of 1.50 Normalized to unity. Normalized to unity. Figures in parentheses are the actual numbers of contacts observed. A.
bonds, it is necessary to determine whether they involve hydrogen bond acceptor atoms. The distribution of atom types involved in the nearest-neighbor contacts is therefore given in Table I1 for (1) all contacts, (2) contacts that are shorter than the sum of the van der Waals radii, i.e. with d > 0.0 A, and ( 3 ) contacts with d > 0.3 A. Also given in Table I1 is the expected distribution of atom types. This is based on the assumption that the probability of a particular (C-)H atom forming its nearest-neighbor contact to an atom of a given type depends only on the stoichiometry of the crystal structure, e.g., P(Y=C) = N J N
Figure 2. Distribution of
(2)
where P(Y=C) is the probability that the nearest-neighbor contact is to a carbon atom, N , is the number of carbon atoms in the asymmetric unit, and N is the total number of atoms in the asymmetric unit.20 The expected distribution was calculated numerically by a Monte Carlo simulation. It should be compared with the observed distribution for all 661 nearest-neighbor contacts because all of the (C-)H atoms in the sample were included in the simulation. Two major results emerge from the figures given in Table 11. The first is that (C-)H--C and (C-)H.-H contacts with d > 0.3 A are uncommon but do exist.21 This shows that the occurrence of a (C-)H-O contact with d > 0.3 8,is not, in itself, conclusive proof of hydrogen bond formation. The second result is that the proportion of nearest-neighbor contacts that involve oxygen atoms is far higher than would be expected from the stoichiometries of the crystal structures studied. The proportion is even larger when only the short nearest-neighbor contacts are considered. Thus, (20) Excluding metal ions. Metal ions were ignored in the calculations because they were also ignored when the observed distribution was derived. (21) The (C-)H.-C and (C-)H-H contacts with d > 0.3 A are HY2.-C in L-glutamine (Table I, 39; note that there is a printing error in this paper: the z coordinate of C should be 0.7250, not 0.7520), H ( 5 ) 4 ( 4 ) in 2-nitro1.3-indandione dihydrate (Table I, 84), and H(20)-H(14) in potassium hydrogen mesotartrate (Table I, 57).
0.00
of the 46 contacts with d > 0.3 A, 42 are of the type (C-)H--O. This is reflected by the fact that the mean value of d for the 289 nearest-neighbor contacts involving oxygen is 0.105 A, compared with a value of 0.030 A for the complete sample. At this stage, it was necessary to eliminate two possibilities: (1) The difference between the observed number of (C-)H-O contacts and that predicted from the stoichiometries of the crystal structures may not be statistically significant. (2) The van der Waals radius used for oxygen may be incorrect. These possibilities are discussed in turn below. (1) Statistical Significance. Consider the ith crystal structure in the sample, and let N , = total number of atoms in the asymmetric unit,20X , = number of oxygen atoms in the asymmetric unit, Hi = number of (C-)H atoms in the asymmetric unit, m, = number of (C-)H atoms in the asymmetric unit that form nearest-neighbor contacts to oxygen atoms. Under the null hypothesis that the (C-)H atoms do not show any preference for forming short intermolecular contacts to oxygen atoms, the probability (a,)that mi or >m, of the nearest-neighbor contacts are of the type (C-)H.-O isz2 J=H,
(ff,!/j
