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Hydrogen-Bonding: An updateGeorge A. Jeffrey aa Department of Crystallography, University of Pittsburgh,Pittsburgh, PA 15260, USAPublished online: 12 May 2010.

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Crystallography Reviews, April–September 2003,

Vol. 9, Nos. 2–3, pp. 135–176

HYDROGEN-BONDING: AN UPDATE

GEORGE A. JEFFREY

Department of Crystallography, University of Pittsburgh, Pittsburgh, PA 15260, USA

(Originally received 17 March 1994; In final form 30 March 1994)

This article focusses on the crystallographic research aimed at a better understanding of hydrogen bondswhich has been published since January 1990. In the interest of continuity, earlier work is quoted when itrelates to that published during this period.

Keywords: Bifurcated; Two-, three- and four-centered bonds; Graph sets; � and � cooperativity; Resonanceassisted hydrogen bonds (RAHB); Proton sponges; C–H� � �O bonds; X–H� � �� bonds; Flip-flop; Tunnelling;Lost bonds; Clathrates; Molecular recognition

Contents

1 CONCEPTS, DEFINITIONS AND CONFIGURATIONS 136

2 PROGRESS IN METHODS 139

3 NETWORKS, MOTIFS AND COOPERATIVITY 142

3.1 Cooperativity and Resonance Assisted Hydrogen Bonding (RAHB) 144

4 METRICAL PROPERTIES OF O–H� � �O, N–H� � �O, N�H � � �N

AND O�H � � �N BONDS

146

4.1 O–H� � �O Bonds 146

4.2 N–H–O Bonds 148

4.3 N–H � � �N Bonds 148

4.4 O–H� � �N Bonds 149

5 STRONG HYDROGEN BONDS AND PROTON SPONGES 150

6 C–H� � �A BONDS 155

7 HYDROGEN-BOND DISORDER; TUNNELLING; FLIP-FLOP;

LOST BONDS

157

ISSN 0889-311X print/ISSN 1476-3508 online � 2003 Taylor & Francis Ltd

DOI: 10.1080/08893110310001621754

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8 HYDROGEN BONDS IN INCLUSION COMPOUNDS 159

9 X–H� � �p BONDS 162

10 MOLECULAR RECOGNITION AND HYDROGEN BONDING 164

11 MISCELLANEOUS 164

References 165

Subject Index 175

1 CONCEPTS, DEFINITIONS AND CONFIGURATIONS

Concepts and definitions developed from when X-ray crystallographers could not seehydrogen atoms still persist in some publications, especially those in the field of molecu-lar biology and protein crystallography where hydrogen atoms are generally still unseen.

The definitions used in this article are given below.The geometry of a hydrogen-bond X–H� � �A involves an X� � �A distance*, which is

a function of an X–H covalent bond-length, an H� � �A hydrogen bond length, andan X–H� � �A hydrogen bond angle. As pointed out by Kroon et al. (1975), this angleis statistically unlikely to be 180� due to the conic correction. When X� � �A distanceshad to be used as the criteria for hydrogen bonding in crystals, it was considerednecessary that they be less than the sum of the van der Waals radii. Since the attractivecomponent of the van der Waals interaction attenuates as r�6, whereas the attractiveelectrostatic component of the hydrogen bond attraction attenuates as r�1, this conceptwas non-sensical. This was made very apparent by the ab-initio (HF-631G*)calculation by Singh and Kollman (1985) of the potential for the water dimer whichwas decomposed into its various components.

In practice, the H� � �A bond lengths in crystals rarely exceed 3.0 A and the X–H� � �Aangles are greater than 90�. The role of the repulsive forces in determining hydrogenbond geometry in the ices and hydrates was discussed by Savage and Finney (1986)and by Savage (1986). The same concepts of an excluded region determined by therepulsive forces will apply to other types of hydrogen bonds. As a consequenceof these repulsive forces, the X� � �A distances tend to remain relatively constant,while permitting large variations in H� � �A bond lengths and angles, as shown inFig. 1. For this reason, hydrogen-bonded O� � �O distances also rarely exceed 3.0 A.Clearly hydrogen-bond distances and angles are a much more sensitive criterion ofhydrogen bonding than the O� � �O or N� � �O distances, despite their lower accuracy.Fortunately NH hydrogen positions can be calculated with reasonable accuracy,when they are not observed experimentally. This is not true for O–H hydrogenatoms. The precision of hydrogen bond lengths can be improved if the O–H or N–Hcovalent bond lengths are normalized to internuclear (i.e. neutron diffraction) values(Jeffrey and Lewis, 1978). A very precise X-ray single crystal analysis of Ice Ih at243K by Goto, Hondok and Mae (1990) gave O–1

2H distances of 0.85(2) and

*Sometimes referred to erroneously as a hydrogen bond length.

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0.82(3) A, corresponding to a displacement of 0.15 to 0.18 A between the electron andFermi density peaks (see however, Kuhs and Lehman, 1983).

The terms bifurcated and three-centered, and sometimes bifurcated three-centered,are used interchangeably in current literature. The term bifurcated was first used inthe X-ray crystal structure analysis of �-glycine by Albrecht and Corey (1939)to describe the configuration I. However, Pimental and McClellan (1960), in thefirst text devoted solely to hydrogen bonding, applied the term to configuration II.This configuration, which only applies to H2O and the NH2 group, is in fact, rarely,if ever, observed in crystals, except as part of three-center bonds.

FIGURE 1 Distribution of Ow–H� � �O angles versus H� � �O bond lengths in some hydrates of small biolo-gical molecules. [from Jeffrey (1992b)]

HYDROGEN BONDING 137

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To avoid confusion in terminology, the term three-centered was introduced for I todescribe the hydrogen bonding in carbohydrate crystals by Ceccarelli, Jeffrey andTaylor (1981) and in amino acid crystals by Jeffrey and Maluszynska (1982) andJeffrey and Mitra (1984). It is a requirement that the hydrogen atom is bonded tothree other atoms, one by a covalent bond and two by hydrogen bonds. The hydrogenatom should therefore lie close to the plane of X, A and A0, so the sum of the threeangles about H should be �360�.

This type of bond occurs frequently (�70%) in the crystal structures of the

zwitterionic amino acids and is attributed to a proton deficiency, since Nþ

H3 hasthree protons and O= �CC=O prefers to accept four hydrogen bonds. Hence theanalogy with electron deficient three-center bonds in the boron hydrides.

A study of three-center NHO=CO=C

bonds in 1509 crystal structures by Taylor,

Kennard and Versichel (1984a, b) found about 20 percent of such bonds.

In the crystal structures of the carbohydrates, nucleosides and nucleotides, purinesand pyrimidines, the proportion of three-center bonds is about 25 percent (Jeffreyand Saenger, 1991). Neutron diffraction studies of the hydrogen bondingin �-cyclodextrin. EtOH � 8H2O (Steiner, Mason and Saenger, 1991) and partially deut-erated �-cyclodextrin 17.7D2O by Ding et al. (1991) showed that 32 percent of thehydrogen bonds were three-centered and 4 percent were four-centered. An extensionto protein crystal structures by an analysis of three-center bonds in thirteen high-reso-lution protein crystal structures is now reported by Preissner, Enger and Saenger(1991). Of the 4974 hydrogen bonds examined, 24 percent were three-centered.However of the 620 peptide N–H� � �O¼C bonds involved in �-helix formation, 92percent are three-centered. The major components are (nþ 4)N–H� � �O¼C(n) bondsof the 3.613 helix and the minor components are (nþ 4)N–H� � �O¼C(nþ 1) bonds inthe 310 helical distortions at the C-termini of the �-helices. In the �-sheets, 40 percentof the bonds are three-centered. The majority of three-center bonds are asymmetrical,with the major components having H� � �O bond lengths from 1.6 to 2.9 A, with angles175 to 90�. The distribution of these bond lengths rises at 1.8 A with a peak at 2.1 A,dropping slowly to 2.6 A. The minor components have bond lengths from 2.05 to3.0 A with angles 175 to 90�, with a maximum in the distribution of a H� � �A distanceof 2.8 A. In the earlier analysis of hydrogen bonding in protein structures by Bakerand Hubbard (1984), X–H� � �A angles from 180 to 90� were considered, but theH� � �O cut-off was at 2.5 A. This would result in 80 percent of the three-center bondsin the �-helices being identified as two-center. As pointed out by Preissner, Engerand Saenger (1991), this is an aspect of hydrogen-bonding that is often inadequatelyconsidered in the computer programs that seek to investigate hydrogen-bonding in pro-tein structures. A study of three-center bonding in a DNA model by moleculardynamics using AMBER concluded that they occurred frequently but were a conse-quence of the polymer geometry rather than structure determining (Fritsch andWesthoff, 1991). The role of bifurcated, i.e. three-centered, hydrogen bonds in stabiliz-ing non-planar amino groups in DNA bases is examined by ab-initio molecular orbitalcalculations at the HF/6-31G*, MP2/6-31G* levels by Sponer and Hobza (1994).

A few configurations were observed in which the hydrogen atom has four acceptoratoms within 3.0 A in the forward direction of the X–H bonds, i.e. X–H� � �A� 90�.There four-center bonds are relatively rare, occurring in the various recent metricalsurveys referred to later in this text at less than 4 percent.

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Other configurations that have been observed, albeit rarely, are III and IV, and thethree and four-center bifurcated combinations V, VI and VII observed in the hydratesof small biological molecules by Jeffrey and Maluszynska (1990) and by Steiner andSaenger (1993a)

2 PROGRESS IN METHODS

Single crystal analysis by neutron diffraction is the experimental method par excellencefor studying the structural aspects of hydrogen bonding in crystals, since it provideshydrogen positions with a precision comparable to that of the non-hydrogen atomstogether with their anisotropic thermal ellipsoids. In addition, any temperaturesdown to � 10K are relatively easily accessible, permitting corrections for thermallibration and anharmonic motion (Jeffrey, 1992a). There has, however, been a declinein the number of single-crystal neutron diffraction studies in recent years due to aregretable hiatus in the availability of suitable steady-state neutron sources. Thefuture availability of more powerful neutron sources should reduce the limitationof crystal size, which has been a significant deterent to the location of hydrogenatoms in complex biological structures. Spallation neutron sources are socially moreacceptable, but the potential of pulsed neutron powder diffraction studies of hydrogenbonding for other than simple structures is uncertain.

The precision of data from X-ray diffractometers and area detectors has improvedand low-temperature single-crystal X-ray analysis with liquid nitrogen has become amore common practice. In consequence, hydrogen atom coordinates with isotropictemperature factors are reported regularly, with an accuracy about ten times lessthan for the non-hydrogen atoms. The reporting of hydrogen-bond geometry in crystalstructure analyses often leaves something to be desired. The practice of reportinghydrogen-bond lengths and angles with respect to a single molecule (symmetry 1,xyz) is equivalent to describing the structure of a molecule by the distances andangles relative to a single pair of atoms. The information is there, but the structuralchemistry (i.e. configuration and conformation) is not obvious. The importance ofthe hydrogen-bond networks, discussed later, requires more attention to this featurein those crystal structures where the cohesive forces between the molecule are primarilyhydrogen bonds.

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The charge-density studies on the crystal structure of formamide by Stevens (1978),and oxalic acid dihydrate by Krijn and Feil (1988) demonstrated the expected displace-ment of the hydrogen or deuterium electron density from the Fermi nuclear density inthe N–H� � �O¼C and O–H� � �Ow hydrogen bonds, giving rise to a dipole of the order of1 Debye at the end of the X–H bond (Craven, 1987). Disengaging the effects of thermalmotion is an undesirable complication in charge density analysis, especially since thetemperature factors from X-ray and neutron analyses at the same temperature havea tendency to disagree. Few laboratories have yet to develop equipment for collectinghigh precision X-ray data down to liquid helium temperatures to match the neutrondiffraction data at that temperature. An exception is the recent analysis of oxalicacid dihydrate and acetamide at 15 and 23K by Zobel et al. (1992) which providedhigh quality X-ray data to complement the neutron diffraction data of Coppens andSabine (1969) and Jeffrey et al. (1980). For acetamide at 23K, the number of uniqueintensites measured and the intensity gain for high order reflections were about fourtimes greater than that from the room temperature analysis.

More recent precision electron density studies have focussed on the generalelectrostatic properties of molecules (Craven and Stewart, 1990). The electrostaticpotential of a molecule, or a group of molecules, which can be derived from an accuratecharge-density distribution (Stewart, 1991), is now considered by some investigators tobe more informative and useful than the deformation density plots. A mathematicalprocedure is described whereby the charge parameters of a pseudoatom model canbe used to map the electrostatic potential and show the polarizing effect of hydrogenbonding, as demonstrated in the crystal structure of �-aminobutyric acid (Stewartand Craven, 1993).

The use of solid-state NMR, particularly C13 cross-polarization magic-anglespinning (CP/MAS) was reviewed in this journal by Etter, Hoye and Vojta (1988).As pointed out in that article, the method is indeed complementary to that of crystalstructure analysis. The identification of three isomeric forms of the disaccharide lactu-lose in the ratio 0.745 : 0.100 : 0.155 by Jeffrey et al. (1983) prompted the suggestion thatthis method of analysis should be applied routinely, whenever there is the possibility ofa molecular mixture in the crystallization solution. It can also be a useful diagnostictool when anomalies are observed in the anisotropic thermal motion parametersfrom a crystal structure analysis and for recognizing co-crystallization of differentmolecules.

Although NMR lH chemical shifts are very sensitive to hydrogen bonding inthe solid-state (Berglund and Vaughan, 1980; Jeffrey and Yeon, 1986), therehas been relatively little recent work using this observation which relates specificallyto hydrogen bonds. In molecules with many C–OH groups such as carbohydrates,differences in the 13C isotropic chemical shifts in the crystals and in solution can bean indication of crystal field and solvation effects (Sastry, Takegoshi and McDowell1987). The strong O–H� � �F hydrogen bond in the complex KF � (CH2COOH)2 wasstudied by a neutron crystal structure analysis and F solid-state NMR (Mortimeret al. 1992). Etter, Reutzel and Vojta (1990) measured the isotropic chemical shift fora number of hydrogen-bonded organic crystals. A study of the short hydrogen bondsin the salts of the dicarboxylic acids by Karlsbeck, Schaumburg and Larsen (1993)used 13C and 2HNMR spectroscopy.

The interesting application of solid-state NMR to single crystals to display(by ORTEP) the anisotropic chemical shift tensors, as exemplified by the studies of

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L-asparagine monohydrate (Naito and McDowell, 1984) and methyl �-D-glucopyrano-side (Sastry, Takegoshi and McDowell, 1987) does not seem to have been continued.Possibly this is because it requires large crystals (cm rather than mm), the combinedskills of a crystallographer and an NMR spectroscopist, and much patience to use amanual single-crystal NMR spectrometer.

Infrared spectroscopy preceded crystallography as a method for studying hydrogenbonds (cf. Pimental and McClellan, 1960; Hadzi and Bratos, 1976) and solid stateFT-IR spectroscopy is a major method which often complements X-ray crystalstructure analysis, for examples in the work of Kanters et al. (1992a) on calixarenesand of Harman, Southworth and Harman (1993) on the tetraethylammonium fluoridehydrates.

The computer accessibility of the Cambridge Crystallographic Data Base hasmade the survey of the structural features of particular types of hydrogen bondingvery convenient (Allen, Kennard and Taylor, 1983; Taylor and Kennard, 1984).Although this method of evaluating the strength of hydrogen bonds from experimentaldata has been criticized by Burgi and Dunitz (1988), most investigators considerthat if it is derived from homogeneous classes of molecules, it can provide reliablequalitative information about hydrogen-bond strengths in crystals that is not readilyavailable from other sources.

Ab-initio quantum mechanics has now reached a level of sophistication that theequilibrium structures of many hydrogen-bonded dimers or trimers can be calculated(cf. Del Bene, 1988; Del Bene and Shavitt, 1991; Ha, Makenewitz and Baudes, 1993).In fact, this is probably now a more precise method for obtaining data on the hydrogen-bond geometries and energies for gas-phase hydrogen-bonding than that by experiment.The water dimer is a popular guinea-pig for testing the finer details of ab-initio MOtheory, such as effects of basis-set deficiency, correlation, basis-set superposition, etc.(cf Kroon-Batenburg and van Duijneveldt, 1985; Saeba, Tong and Pulay, 1992).It must be frustrating for the proponents of this art that the cancellation of errorsis such that the more approximate calculations frequently seem to provide resultsthat agree better with experiment. The extensive use of acronyms makes this fielddifficult for the non-specialist to understand, but the impression is that theory nowgives results within the experimental error bars for the distances and angles involved,when appropriate corrections are made for the effects of anharmonicity (i.e. O� � �O¼

2.976� 0.006 A in the water dimer). Because the potential energy surface is so flat,there seems to be less certainty about the actual location of the hydrogen-bondinghydrogen atom.

Semi-empirical methods are generally not very satisfactory for predicting hydrogenbond geometries and energies. However, good agreement with experiment has beenobtained using a modified MNDO method when applied to a number of structureswith short intramolecular O–H� � �O bonds (Rodrıguez, 1994).

There have been many calculations of the equilibrium geometries of other hydrogen-bonding dimers which are published in a variety of journals. The number is suchthat a computerized data base for them would now be useful to the non-specialists inthis field, including the crystallographer, who might like to systematically comparehydrogen bonding in the gas-phase with that in a crystal (i.e. to study the crystalshrinking effect).

The theoretical treatment of hydrogen bonding is implicit in the empirical force fieldsused in molecular mechanics or molecular dynamics which are becoming increasingly

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popular for predicting the structures of large molecules, such as oligonucleotides,peptides, saccharides, proteins and nucleic acids, and for predicting molecularinteractions and solvation effects. The Allinger molecular mechanics programs(MMn) use dipole-dipole interactions but other methods, including the popularmolecular dynamics programs CHARMM and GROMOS, rely on charges on thedonor and acceptor atoms. Calculations on carbohydrate structures are especiallysensitive to the treatment of hydrogen bonding because of the high ratio ofhydrogen-bonding groups in these molecules. They therefore provide excellent testsfor the credibility of molecular mechanics and dynamics simulations (cf. van Eijck,Kroon-Batenburg and Kroon, 1990; Koehler, 1991; French and Miller, 1994).When these methods are applied to the same or similar carbohydrate problems theydo not always give the same result. For example, the simulation of the structureof �-D-glucopyranose in water using CHARMM by Brady (1989) gave results whichdiffered from those on �-D-glucopyranose in water by van Eijck, Kroon-Batenburgand Kroon (1990), by more than would be expected from the difference between thetwo anomers.

Various site models and different hydrogen-bond potentials for liquid water andliquid methanol were tested against molar volume, heat of vaporization and the neutronweighted radial distribution curves using the molecular dynamics program GROMOS(Stouten and Kroon, 1988; Stouten, van Eijck and Kroon, 1991). Reasonable agreementwas obtained. All gave O� � �O distance distributions between 2.5 and 3.5 A with maximaat �2.75 A. A study of the structure and dynamics of Ice Ih by means of moleculardynamics is reported by Sciortino and Corongiu (1993).

Theoretical calculations on isolated molecules containing near neighbouring donorand acceptor groups will predict intramolecular hydrogen bonding which is not presentin the crystal or in aqueous solution. In carbohydrates, for example, the C–C–O–Htorsion angles had to be fixed at crystal structure angles to prevent intramolecularhydrogen bonding in some early molecular mechanics calculations (Jeffrey andTaylor, 1980). This problem is now overcome to some degree by using molecularmechanics to predict carbohydrate structures and hydrogen bonding in the presenceof water molecules (e.g. Kroon-Batenburg and Kanters, 1983), or by constructingmini-crystals (e.g. French, Miller and Aabloo, 1993), or by simulating solvent effectsby molecular dynamics (van Eijck, Kroon-Batenburg and Kroon, 1990). For carbohy-drates where the ratio of hydrogen-bonding donors and acceptors is equal to thenumber of carbon atoms (Cn(H2O)n), satisfactory solutions are still being sought (cf.Kounijzen et al., 1993; Bouke et al., 1993; Grootenhuis and Haasnoot, 1993; Frenchand Miller, 1994). For nucleic acids and proteins and their components where theratio of hydrogen-bonding functional groups to van der Waals interactions is less,the problem of simulation should be less severe, since the van der Waals potential isbetter understood. However, although there has been much more research, the resultsseem to be similar with some successes and some failures (Teeter, 1991).

3 NETWORKS, MOTIFS AND COOPERATIVITY

In deriving a graph-set approach to rationalizing hydrogen bonding, Etter (1990)defined a network as a subset of an array of molecules in which each moleculeis connected to another by at least one hydrogen-bonded pathway. A motif is then a

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network in which there is only one type of hydrogen bond. Hydrogen-bonding motifsare familiar concepts in the ices and the clathrate hydrates, since the water moleculesare linked only by Ow–H� � �Ow bonds. The chains and loops which occur in carbohy-drates and carbohydrate hydrates are, by this definition, networks, since the moleculesare linked by combinations of O–H and Ow–H as donors, and O–H, OwH, and O asacceptors (Jeffrey, 1992b).

Cooperativity or non-additivity, occurs when the hydrogen-bond energy of a networkor motif is greater than the sum of the energy of the individual hydrogen bonds:

EðH � � �AÞn > nEðH � � �AÞ:

Two types of cooperativity have been recognized: �-cooperativity, where the hydrogenbonds are linked by covalent O–H bonds, and �-cooperativity or Resonance AssistedHydrogen Bonding* (RAHB), where the hydrogen bonds are linked by both X–Hbonds and multiple C::::��N or C::::��O covalent bonds (Gilli et al., 1989).

The graph theory method of describing hydrogen bond networks uses captial letters(S, C, R, D) to distinguish between inter- and intramolecular bonds and whether theyform finite or infinite chains or rings (S¼ intramolecular; C¼ infinite chains; R¼ rings;D¼ non-cyclic dimers and finite chains). Numerical super and subscripts give thenumber of different kinds of donors and acceptors. A parameter in parentheses (r)gives the number of atoms in the ring or the repeat length of the chain includingcovalent bonds. This procedure identifies hydrogen bonding as a distinct configuration.For example, the Watson-Crick bonding VIII is R2

2ð8ÞO4, whereas the Hoogsteenbonding IX is R2

2ð9ÞO4 (Etter, Mac Donald and Bernstein, 1990). More complex net-works may require several sets of symbols, i.e. first, second and third order, and forcomplex networks the choice may not be unique.

Hitherto the application of graph set analysis has been relatively limited (Bernstein,1991; Bernstein and Shimoni, 1993). Clearly a wider application would be very usefulfor identifying common components of networks or motifs in crystal structures of mol-ecules which are chemically unrelated. This would be especially so if this informationwere included where appropriate, in a sub-set of the Cambridge CrystallographicData Base. The recognition of common hydrogen-bonding preferences is impor-tant since it can be used to design complexes with special properties and predictable

*By analogy, �-cooperativity could be called Polarization Assisted Hydrogen Bonding; in both casesEnhanced would be a better word than Assisted.

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symmetry by co-crystallization (Etter and Frankenbach, 1989). It could play a role inpredicting the molecular recognition discussed later.

For the carbohydrates, carbohydrate hydrates, including the cyclodextrins, themajority of the hydrogen-bond functional groups, O–H, Ow–H, are both donors andacceptors. The networks are formed by finite chains, infinite chains and rings. Whenring or glycosidic oxygens are included, they act as chain stoppers (Jeffrey and Mitra,1983). In the hydrates, the dual acceptor/donor functionality of the water moleculeslinks the chains to form three-dimensional nets, or when single acceptor/doubledonor, branched chains (Jeffrey, 1992b). These hydrogen-bond structures can thereforebe described by means of connectivity diagrams which link the sequences of O–H andH� � �O hydrogen bonds. These diagrams of the hydrogen-bond structure are equivalentto the configurational diagrams of structural chemistry.

Both the graph theory and the connectivity diagrams have the disadvantage thatthey do not display the conformation of the hydrogen-bond structure that isprovided by stereoviews or computer graphics. However, the bond lengths, bondangles and symmetry operations can be applied to make the connectivity diagramsmore informational. This information is lost in the graph-theory approach, where thesymbolism is one step further removed from the three-dimensional structure.

3.1 Cooperativity and Resonance Assisted Hydrogen Bonding (RAHB)

Neither �-cooperativity nor RAHB are new concepts. The �-cooperativity or non-additivity property of the hydrogen bonding in water was known conceptually formore than thirty years (Kavenau, 1964) and quantitatively from the early ab-initiocalculations on water trimers by Hankins, Moskowitz and Stillinger (1970) and byDel Bene and Pople (1970) on cyclic water polymers. The energetic advantage ofsequential � � �O–H� � �O–H� � �O–H� � � hydrogen bonding indicated by these early calcu-lations led to the distinction between homodromic, antidromic and heterodromic descrip-tors to describe the cyclic patterns of hydrogen bonds observed in the cyclodextrinhydrates (Saenger, 1979; Koehler, Lesyng and Saenger, 1987; Lesyng and Saenger,1981). An analysis of the effect of cooperativity on the H� � �O bond lengths from neu-tron diffraction studies of carbohydrates, mostly monosaccharides, by Ceccarelli,Jeffrey and Taylor (1981) showed that the bonds in chains were about 0.07 A shorterthan isolated bonds. A barely significant shortening of � 0.01 A in the covalent O–Hbond lengths has been detected by Steiner and Saenger (1992a) from low-temperatureneutron diffraction data from two deuterated �-cyclodextrin hydrates (�-CD.11.6D2Oat 120K; �-CD.EtOD 8H2O at 12K). They find a linear correlation from O–H, H� � �O0.985, 1.70 A to 0.96, 2.1 A. They also observed a shortening of O–H bond lengths as aresult of three-center bonding.

RAHB was apparent from the effect of dimer hydrogen bonding on the carboxylicacid bond lengths of formic, acetic and propronic acids studied by gas diffraction byAlmenninger, Bastiansen and Motzfeld (1969) and Derissen (1971). Ab-initio calcula-tions on the monomers and hydrogen-bonded dimer of formamide predicted theeffect of hydrogen bonding in shortening the length of the C–N bond (by 0.023 A)and lengthening the C¼O bond (by 0.018 A) (Jeffrey et al., 1981). Similarly the dimerand chain-type of hydrogen bonding observed in the crystal structures of bothcarboxylic acids (X) and oximes (XI) are accompanied by significant increase in the

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� character of the adjacent C–O and C–N bond lengths (Bachechi and Zambonelli,1972, 1973; Brahm and Watson, 1972 and references therein).

The descriptor RAHB has now been applied to this effect in some carboxylic acidoximes containing the chain XII or cyclic configuration XIII (Padmanabhan, Pauland Curtin, 1989; Maurin, Paul and Curtin, 1992a, b, 1994; Maurin et al., 1993;Maurin, Winnicka-Maurin and Les, 1993).

An interesting study of the RAHB effect of electron supplying and withdrawingsubstituents on the intramolecular hydrogen bond in malonaldehyde has been studiedby ab-initio molecular orbital theory at the 3-21G level by Rios and Rodriguez (1991).

It was the neutron diffraction studies of the monosaccharides by Jeffrey and Takagi(1978) and of the cyclodextrins by Saenger and co-workers (KIar, Hingerty andSaenger, 1980) that generalized �-cooperativity from water to carbohydrate structures.Similarly it was the work of Gilli et al. (1989; 1993a) on hydrogen bonding involving theO¼C–C¼C–OH moiety in �-diketones which led to the introduction of the termRAHB. More recently, this concept has been extended to the hydrogen bondingbetween molecules containing O¼C–C¼C–NH and O¼C–C¼N–NH moieties(Ferretti et al., 1993). Whereas the �-cooperativity involves the polarization ofthe relatively weak and essentially electrostatic hydrogen-bond interactions, the �or RAHB cooperativity occurs with strong hydrogen bonds and is consideredby Gilli et al. (1989, 1993a, 1993b) to involve a significant covalent, i.e. exchange,component.

�-cooperativity is important in the hydrogen bonding in carbohydrates and hydrates,including the ices. RAHB or �-cooperativity plays an important role in the structure ofproteins and nucleic acids, not only by strengthening the hydrogen bonds but also byincreasing the �-bonding component and hence the torsional rigidity of the peptideC–N bonds.

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4 METRICAL PROPERTIES OF O–H� � �O, N–H� � �O, N�H � � �N

AND O�H � � �N BONDS

4.1 O–H� � �O Bonds

The relative abundance of both neutron and X-ray diffration studies from carbohy-drates, oxyacids and their salts and hydrates has made the O–H� � �O bond the moststudied of all hydrogen bonds. The H� � �O bond lengths range from the short symme-trical almost linear bonds of 1.215 to 1.230 A to the minor components of three-centerbonds in the range of 2.0 to 3.0 A, with O–H� � �O angles approaching 90� (Jeffrey andSaenger, 1991; Jeffrey, 1992b). A further study by Steiner and Saenger (1992b) of O–H� � �O bonds in carbohydrates has extended the limits of enquiry to H� � �O<5.0 Aand angles from 0 to 180�. The data set contained 110 hydroxyl, 53 ether oxygensand 16 water molecules, from 17 neutron diffraction crystals structures, includingtwo high-resolution studies of hydrated � cyclodextrin structures. Partially occupiedor orientationally disordered donor or acceptor groups were excluded and there wereno corrections for the thermal motion of the hydrogen atoms. The plot of H� � �O vsO�bHH � � �O to 5.0 A and 90� irrespective of hydrogen-bond formation is shown in Fig.2. There are six regions: (1) is the two-center and major components of three-centerbonds; (2) is the minor components of three-center and a few four-center bonds; (3)is non-bonding second neighbours; (4) a random scatter of non-bonding second neigh-bours; (5) a sparcely populated region of nearly linear stretched bonds; (6) the region

FIGURE 2 Scatterplot of O–H� � �O angles versus H� � �O bond lengths for hydroxyl and water donors incarbohydrate crystal structures.(1) two-center and major component of three-center bonds.(2) minor components of three- (and four-) center bonds.(3) non-bonding next neighbours.(4) non-bonding second-next neighbours.(5) near-linear stretched bonds.(6) excluded region due to repulsive forces. [from Steiner and Saenger (1992b), with permission.]

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excluded by O� � �O repulsions (Savage and Finney, 1986). Note that regions (1) and (3),bonding and non-bonding with the same O� � �O distances, cannot be distinguished with-out knowledge of the positions of the hydrogen atoms, (i.e. O–H� � �O angles h90�i) whencelies the confusion from relying on, and reporting only, O� � �O separations to identifyhydrogen bonds. It is one of the reasons why it is so difficult to identify hydrogen-bond-ing networks in the bound water of protein crystals.

Water molecules have less crystal packing constraints than larger moleculeswhere compromises have to be made to minimize the sum of the energies of bothhydrogen-bond and van der Waals interactions. The O–H� � �O vs H� � �O plot, Fig. 3,for hydroxyl and water donors only, although less populated, showed the samefeatures, except that there were no stretched bonds. It would have been interestingto compare the plots for water donors and acceptors separately, since bond lengthconsiderations suggest that water molecules are stronger acceptors than they aredonors (Jeffrey and Saenger, 1991). In two further studies, the correlationbetween O–H, H� � �O, O� � �O distances and O–H� � �O angles was made using onlyhigh precision low-temperature neutron diffraction analysis. One, by Steinerand Saenger (1992a), was based on the data from two deuterium substituted�-cyclodextrin complexes, �-CD, 11.6D2O (Zabel, Saenger and Mason, 1986), and �-CD �EtOH � 8D2O (Steiner, Mason and Saenger, 1990). The other, by Steiner andSaenger (1993a), was of a wide variety of molecules and included both charged anduncharged O–H� � �O bonds.

The cyclodextrin-based paper by Steiner and Saenger (1992a) focussed on thevariation in length of the covalent O–H bonds and the effect of three-center andcooperative hydrogen bonding. The paper by Steiner and Saenger (1993a) based onthe 23 more general crystal structures examined the correlations between O–H,

FIGURE 3 Scatterplot O–H� � �O angles with versus O� � �O distances for hydroxyl and water donors incarbohydrate crystal structures. Numbered regions as in Fig. 2. [from Steiner and Saenger (1992b), withpermission.]

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H� � �O, O� � �O distances and angles. In both papers, the use of low temperatures (15Kor 120K) reduced the uncertainties in O–H bond lengths due to thermal motion. Thelower-bound and riding-motion models of Busing and Levy (1964) were used for thecyclodextrin data. The corrections were small, with a mean shift of þ 0.015 A forthe riding-motion model. No corrections were made for anharmonic motion, whichtends to compensate for the harmonic correction at low temperatures (Jeffrey,1992a). With these corrections, the plot of O–D vs D� � �O showed a decrease of O–Dfrom 0.99 to 0.965 A with H� � �O from 1.70 to 2.15 A. There was evidence of a smalleffect of cooperativity on the covalent O–D bond lengths resulting in a lengtheningof about 0.01 A.

In the more general paper by Steiner and Saenger (1993a), the small corrections forthermal motion were not included. Plots of O–H vs H� � �O extended from 1.19 to 0.95 Aand 1.20 to 2.21 A respectively. They were smoother than previously reported (Jeffreyand Saenger, 1991), especially for the shorter bond lengths. No dependency of covalentO–H bond length on O–H� � �O bond angle was detected. No significant differences dueto deuteration were observed.

4.2 N–H–O Bonds

The N–H� � �O bonds include the important N–H� � �O¼C polypeptide bond.Unfortunately, there has been no update of the very general survey of 1509N–H� � �O¼C bonds in 889 crystal structures made by Taylor, Kennard and Versichel(1984b). This survey used a limit of H� � �O<2.4 A, which is more restrictive than thatcurrently used. It was possible to distinguish between donors ranging from R3NHþ

3

to N�H and acceptors from O¼ �CC¼O to O¼CC

C, with mean hydrogen bond lengths

for each of the 24 different combinations from 1.72 to 1.99 A. The donor and acceptorproperties of N–H and O¼C groups in 15 protein structures were reported by Bakerand Hubbard (1984). Since N–H hydrogen positions can be calculated fromthe adjacent bonded atoms, a new metrical study taking into accountthe three-center bonding described by Preissner, Enger and Saenger (1991) should bepossible.

Surveys of N–H� � �O bonds generally were made from the crystal structuresof nucleosides and nucleotides by Jeffrey, Maluszynska and Mitra (1985) and inbarbiturates, purines and pyrimidines by Jeffrey and Maluszynska (1986). The majorityof these structures were room-temperature X-ray analyses and few were high precision.

The analyses covered �Nþ

H3 or Nþ

H4, Nþ

H, NH, �N(H)H as donors of decreasing

strength, and O¼�PP, HOwH, O¼ �CC, OC

Hand O

C

Cas acceptors with decreasing

strength. The range of H� � �O bond lengths was 1.58 to 2.59 A. There are still insuffi-cient neutron diffraction or high precision low-temperature X-ray analyses to refinethese results as was done for the O–H� � �O bonds.

4.3 N–H � � �N Bonds

Surveys of the geometry of N–H� � �N with N�H and �NH2 and donors, N asacceptors and O�H � � �N bonds have been reported by Llamas-Saiz and Foces-Foces (1990) and by Llamas-Saiz et al. (1992). The former used the Cambridge Data

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Base to obtain 307 bonds, with a cut-off at N� � �N<3.2 A and N–H� � �N>140�.The angle constraint will exclude the minor components of three-center bonds, corre-sponding to the equivalent of region (2) in Fig. 2. For the N–H� � �O bonds, therewere 304 N–H� � �OH and 120 N–H� � �Ow. The constraints were N� � �O<3.1 A andN–H� � �O>140�, again excluding the minor components of three-center bonds.

The ranges of H� � �N and H� � �O distances are given in Table I and compared with thevalues reported by Jeffrey (1989) from the crystal structures of purines and pyrimidines(P & P) which provided 773 bonds and from the nucleosides and nucleotides(N & N) which provided 710 bonds. The agreement was as good as might be expectedin view of the different types of molecules involved.

4.4 O–H� � �N Bonds

A survey of the geometry of O–H� � �N and Ow–H� � �N has been reported by Llamas-Saiz et al. (1992), based on the Cambridge Structural Data Base of January 1990. Allclasses of compounds were included except for those containing metals. The datawere restricted to O� � �N distances less than 3.1 A and O–H� � �N angles greater than140�. Therefore the minor components of three-center bonds with H� � �N>201 A andO–H� � �N angles less then 140� were excluded from the survey. 304 O–H� � �N bondsand 120 Ow-H bonds were included. Using normalized O–H bond lengths (0.97 A forO–H, 0.96 A for Ow–H), the mean, minimum and maximum values for the H� � �Nbond lengths and O–H� � �N angles are given in Table I. These are compared withvalues from the crystal structures of nucleosides and nucleotides by Jeffrey (1989).Although the mean values are in reasonable agreement, the ranges differ significantly,illustrating the danger of extending statistical analyses outside particular classes of clo-sely related molecules.

TABLE I Comparison of N–H� � �N and N–H� � �O hydrogen bond lengths from two independent surveysa

From Llamas-Diazand Foces-Foces

(1990)

P&P2-center and

components of 3-centerJeffrey (1989)

N and N2-center and

components of 3-centerJeffrey (1989)

R–NH2� � �NH� � �N (A) mean 2.06 2.02b 2.13

min 1.83 1.85 1.89max 2.30 2.28 2.76

N–H� � �NH� � �N (A) mean 1.96 1.93c 1.88

min 1.75 1.73 1.78max 2.32 2.23 1.99

C–O–H� � �NH� � �N (A) mean 1.87 1.83 1.89

min 1.59 1.71 1.77max 2.18 2.01 2.62

Ow–H� � �NH� � �N (A) mean 1.96 1.99d 1.94

min 1.76 1.78 1.85max 2.19 2.84 2.16

aAll N–H bonds normalized.bExcluding three 3-center bonds with N–H� � �N<140�.cExcluding one 3-center bonds with N–H� � �N<140�.dExcluding one 3-center bonds with Ow–H� � �N<140�. Including one major component of 3-center bond¼ 2.84 A.

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Attention has also been directed to the orientational properties of hydrogen bond

acceptor groups. Earlier studies examined the acceptor properties of C¼O and OC

Coxygen atoms and found a broad spread of acceptor angles (Taylor, Kennard andVersichel, 1983; Murray-Rust and Glusker, 1984). The study of the stereochemistryof water molecules in the hydrates of small biological molecules by Jeffrey andMaluszynska (1990) showed that single acceptor water oxygen atoms had coordinationsranging from pyramidal to planar with no sharp demarcation. These analyses did notconsider C–H� � �Ow bonds, which greatly reduce the number of three-coordinatedwaters. Even when a C–H hydrogen bond does complete the tetrahedral coordination,it can be very distorted (Steiner and Saenger, 1993c).

A study of the nitrogen acceptor angles in O–H� � �N(sp2) hydrogen bondswith O� � �N<31 A and O–H� � �N>140� (Llamas-Saiz et al., 1992) showed a broaddistribution of acceptor angles with the majority within � 30� of the sp2 lone-pairaxis. The distance and angle cut-off eliminated the consideration of the minor compon-ents of three-center bonds. A comparison was made with the results from ab-initio HF/3.21G calculations for 72 pyridine-water hydrogen-bond interactions.

5 STRONG HYDROGEN BONDS AND PROTON SPONGES

Strong hydrogen bonds have characteristic physical properties which distinguishthem from normal or weak hydrogen bonds (Emsley, 1980). They have been studiedby crystal structure analysis since the beginnings of single crystal neutron diffraction.Ellison and Levy (1965) reported a strong symmetrical O� � �H� � � �OO bond in potassiumhydrogen chloromaleate with O� � �H bond lengths of 1.1999(5) and 1.206(5) A. Theshort O� � �H� � � �OO bond in the anion of imidazolium maleate (James and Matsushima,1976) was studied by neutron diffraction leading to an X–N deformation density analy-sis by Hsu and Schlemper (1980). Their results supported the suggestion of a singleminimum hydrogen-bond potential made earlier from the IR spectra by Cardwell,Dunitz and Orgel (1953).

However the other strong O� � �H� � � �OO hydrogen bonds in organic anions have beenshown by neutron diffraction analysis to be unsymmetrical or have double minimaacross a center or two-fold axis of symmetry. These were distinguished assymmetry-free by Olovsson, Olovsson and Lehman (1984), and type A, symmetry-restricted by Currie and Speakman (1970), Catti and Ferraris (1976); see Tables 7.2and 7.3 in Jeffrey and Saenger (1991).

More recent examples of short intramolecular O� � �H� � � �OO bonds are found in a neu-tron diffraction study of hydrogen-bonded dimers in K5[H{ON(SO3)2}2]H2O byRobertson et al. (1988) and in the anions of caronic acid (3,3-dimethylcyclopropane1,2-dicarboxylic acid). The acid crystallizes in cis and trans forms with the usualcarboxylic acid dimer hydrogen bonding with H� � �O bond lengths � 1.7 A (Jessen,1992). In the ammonium and potassium hydrogen salts, the anions, XIV, have strongasymmetrical intramolecular O� � �H� � � �OO bonds with H� � �O and O–H bond lengths of1.47(6), 1.01(6) and 1.35(4), 1.08(4) A respectively (Kuppers and Jessen, 1993).

Strong intramolecular O–H� � �O bonds are also formed in the absence of deprotoni-zation when the oxygen atoms are constrained to short distances due to the molecularconfiguration, as in the �-diketo-enols (XV). The crystal structures of two of these

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compounds were studied by X-ray and neutron diffraction analyses by Jones (1976a, b),and Bertolasi et al. (1991) have added eight more X-ray crystal structure analyses. Asshown in Table II, the H� � �O bond lengths range from normal, 1.70 A, to short, 1.32 A,with a corresponding almost linear correlation with the covalent O–H bond lengths.The O� � �O separations are less systematic, indicating variations in the O–H� � �Oangles. This suggests a quite flat asymmetrical potential well for the hydrogen atom,which is sensitive both to the RAHB effect and the crystal environment.

Pentachlorophenol forms strong hydrogen bonds when complexed with N- andO-bases which have been studied by Wozniak et al. (1991). There is a correspondingshortening of the C–O(H) bond lengths between 1.267 and 1.341 A, and a closing ofthe aromatic ipso angles from 118 to 113�. The adjacent C::::��C bond lengths rangebetween 1.335 and 1.416 A. There are roughly linear relationships between pairs ofthese dimensions.

TABLE II Intramolecular hydrogen-bond geometries in 1,3-diaryl-1-hydroxy-3-keto-propanes (1,3-propane dione enols)

Compound H� � �O (A) O–H (A) O� � �O (A)

1 1.70 0.91 2.5542A 1.53 0.98 2.4323 1.49 1.07 2.5024 1.42 1.10 2.4995 1.39 1.10 2.4346 1.38 1.12 2.4057 1.37 1.15 2.4708 1.36 1.16 2.4639 1.35 1.20 2.49210 1.33 1.20 2.40111 1.32 1.24 2.489�(O-H) and (H� � �O)� 0.01 A, �(O� � �O)� 0.004 A

1 1-mesityl-3-(O-nitrophenyl)2 & 5 1-(p-methoxyphenyl)-3-(m-nitrophenyl)-3 1-(p-nitrophenyl)-3-mesityl-4 1-mesityl-3-(p-methoxyphenyl)-6 1-phenyl-3-(p-nitrophenyl)-7 1-phenyl-3-(p-methoxyphenyl)-8 1-phenyl-3-phenyl- (by neutron diffraction)9 1-mesityl-3-(m-nitrophenyl)-10 1-phenyl-3-mesityl11 1-phenyl-

Compounds 8 and 11 (Jones, 1976a, b). All other compounds, Bertolasi et al. (1991).

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Crystallographic interest in strong hydrogen bonds was further stimulated by thediscovery of the so-called proton sponges*. These are fused-ring aromatic diamineswith exceptionally high basicity due to the close proximity of the basic centers(Alder et al., 1968); Staub, Saupe and Kruger, 1983; Saupe, Kruger and Staub, 1986;Staub and Saupe, 1988). Examples are 4,5-bis (dimethylamine) fluorine, XVI, 4,5-bis(dimethylamine)phenanthrine, XVII, 1,8-bis-(dimethylamine)naphthalene, XVIII.

These molecules with short constrained N� � �N separations can gain a proton tobecome a cation with the formation of a strong N

þ

–H� � �N hydrogen bond. This is thereverse of the strong anionic O–H� � � �OO bonds discussed above. IR spectroscopy suggeststhat these strong bonds are formed in solution as well as in crystals (Pawelka andZeegers-Nuyskens, 1989; Brzezinski et al., 1990).

In the crystal structure of DMAN, the naphthalene ring is distorted from planarsuch that the two nitrogen atoms are 0.4 A either side of the mean plane resulting in anon-bonding N� � �N separation of 2.792(8) A (Einspar et al., 1973). In the many[DMANH]þ salts for which there are crystal structures, see Table III, the naphthalene

ring distortion is much less and the Nþ

� � � ðHÞ � � �N separations range from 2.55 to 2.65 A.

As with the O–H� � �O and O–H� � � �OO hydrogen bonds, the Nþ

� � �N separations are rela-tively constant, but the hydrogen bond lengths vary by 0.5 A, accompanied by a changein the covalent N–H bond lengths by 0.4 A, see Table III. Some of the bonds are disor-dered N–1

2H � � � 1

2H–N with or without a crystallographic symmetry element. In the

absence of a symmetry element, the two sites are not equally populated. In the later crys-tal structure analyses carried out at 100K, the hydrogen electron densities were resolvedby difference Fouriers, indicating a rather flat asymmetric double minimum potential.

Generally the anions and hydrated anions from a separated hydrogen-bondednetwork, but in two structures, [DMANH]þ[Hsquarate]� and the tetrahydrate, thereare weak hydrogen bond linkages through minor three-center components from theN–H� � �N bond, see Fig. 4. In the Hsquarate, it is N–H� � �O¼C with H� � �O¼ 2.85 A,N–H� � �O¼ 108�. In the tetrahydrate, where the N–1

2H � � � 1

2H–N bond is crystallo-

graphically disordered, they are Nþ

�H � � �O¼C and N–H� � �Ow, 2.15, 2.55 A, 103,113�, respectively. In [DMANH]þ 3,4-furan-dicarboxylate, the transfer of the protonresults in both a strong N–H� � �N bond and also a strong O–H� � � �OO bond withO–H¼ 1.04(3), H� � �O¼ 1.44(3) A and O–H� � �O¼ 167(3)�.

A strong unsymmetrical Nþ

�H � � �N bond between a cation and a molecule,

XIX, is observed in phthalazine semi-tetrafluoroborate with Nþ

�H ¼ 1:07ð2Þ and

H� � �N¼ 1.63(2) A.

*A name introduced by Aldrich Chemical Company for [DMANH]þ.

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In phthalazine 1-methyl-5-tetraazothionate, the N–12H � � � 1

2H–N bond is symmetrical

with disordered hydrogens (Wozniak, Krygowski and Grech, 1992). A strong symme-trical [N� � �H� � �N]þ bond with N� � �H¼ 1.317 (1) A and N� � �N¼ 2.635 A was observedby low-temperature neutron diffraction in hydrogen diquinuclidinone, XX, by Roziere,Bilen and Lehman (1982).

TABLE III Hydrogen-bond lengths in the [DMANH]þ cations

Anion N� � �N H� � �Nþ

N–H N–H� � �Nþ

Ref

BF4� 2.562(x) (1.31 m 1.31) 159 a

Br� 2.554(5) (1.31 m 1.31) 153(3) b[tetrazole]�H2O 2.573(2) (1.312) 1.312(5) 157(2) cOTeF5

� (triclinic) 2.574(�) 1.46(�) 1.17(�) 159(�) d(orthorhombic) (1.37m 1.37) 140(3) d0

[tris(hexafluoracetato]�3 Cu2þ 2.65(2) 1.48(17) 1.27(21) 148(12) e[2,4-dinitroimidazolate]�1 2.606(3) 1.48(3) 1.18(3) 160(3) f[pentachlorophenolate]� 2.555(3) 1.49(2) 1.11(2) 162(2) g[pentachlorophenol] at 100K

[1-oxo-2-phenyl 1,2-dicarbo-dodecaborate]�

2.577(3) 1.50(3) 1.22(3) 140(3) h

[chloranilate]�2H2O at 295K 2.589(3) 1.51(3) 1.14(3) 155(2) iat 150K 2.588(2) 1.59(3) 1.07(3) 152(2)

[pentaflurophenolate]� 2.565(3) 1.56(6)* 154(6) j[pentaflurophenol] at 100K 1.84(7) 141(6)

[hydrogen squarate]� 2.583(2) 1.59(2) 1.08(2) 157(2) k[3,4-furan dicarboxylate]� 2.621(3) 1.62(3) 1.06(2) 155(2) l[tris(hexafluoracetato]�3Mg2þ 2.60(1) 1.63(11) 1.25(11) 134(8) e1,8-bis(4-toluenesulphonamido)-2,4,5,7-tetranitronaphthalene

2.610(5) 1.63(5) 1.05(5) 152(5) m

[hydrogen squarate]�2 4H2O 2.594(3) 1.66(6)* 0.97(6) 162(5) nat 100K 2.574(3) 1.69(6)* 0.94(6) 156(5)

[dihydrogen hemimellitate]�0.5H2O 2.604(2) 1.72(2)** 0.94(3) 155(2) oat 100K 1.72** 0.94(6) 164(5)

[D-hydrogentartrate]� 3H2O 2.610 1.75(5)y 0.91(5)y 157(5) pat 100K 1.8y 0.8(1) 160(10)

8-dimethylaminomethyl-1- 2.629(2) 1.61(3)z 1.04(3) 165(3) qdimethylammoniomethyl-naphthalene nitrate at 100K 183(5)z 0.83(6) 161(5)

*m¼mirror symmetry*H disordered over two sites in 0.54:0.46 ratio.**H disordered over two sites in 0.7:0.3 ratioyH disordered over two sites in 0.71:0.29 ratio.zH disordered over two sites in 0.66:0.34 ratioRef.(a) Woznial et al. (1990).(b) Pyzalska, Pyzalska and Borowiak (1983).(c) Glowiak et al. (1992).(d) Miller et al. (1988).(d’) Kellett, Anderson and Strauss (1989).(e) Truter and Vickery (1972).(f) Glowiak et al. (1987).(g) Kanters et al. (1992b).(h) Brown et al. (1987).(i) Kanters et al. (1991b).(j) Odiaga et al. (1992).(k) Kanters et al. (1991c).(l) Glowiak et al. (1993).(m) Malarski et al. (1990).(n) Kanters et al. (1990c).(o) Raves, Kanters and Grech (1992).(p) Israel, Kanters and Grech (1992).(q) Salas, Kanters and Grech (1992).

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FIGURE 4 Top: Unsymmetrical Nþ

–H� � �N bond in [DMANH]þ[squarate]� complex. Bottom: SymmetricalN–(H)–(H)–N bond in [DMANH]þ½squarate�2� 4H2O. [from Kanters et al. (1991c, 1992c) with permission.]

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In the complex of 1,8-bis(dimethylamino)naphthalene with 1,8-bis(4-toluenesulphon-amido)-2,4,5,7-tetranitronaphthalene, the H� � �N� hydrogen bond in the anion issignificantly longer than that in the cation (Table IV). The [N–H–N]� geometry isN�

� � �N¼ 2.600(5) A, H� � �N�¼ 1.85(5) A, N–H¼ 0.82(5) A, N�H� � �N� 153(5)�, while

the N� � �N separations are much the same. The relationship between the crystal fieldenvironment and the location of the hydrogen atom in the N–H� � �N and N–H� � �N�

potential functions presents an interesting challenge for both crystallographers andtheoreticians.

6 C–H� � �A BONDS

The discussion of C–H groups as hydrogen bond donors has recurred. Biologicalmacromolecules, where the hydrogen bond acceptor functionality often exceeds thatof the donors, contain many methylene and methyl groups. It is therefore of interestto ascertain whether C–H� � �O hydrogen bonds could influence molecular conforma-tions and inter-molecular interactions. Should they be included in the computationalmethods that attempt to predict intermolecular interactions? The C–H� � �O hydrogenbond was first suggested as a chemical bond by Glasstone (1937) as an explanationfor the deviations from ideal properties of mixtures of chloroform and acetone ordiethyl ether. This hydrogen bond was enthusiastically sponsored by Sutor (1962,1963) and denounced by Donohue (1968). The strongest evidence for C–H� � �A hydro-gen bonding has come consistently from infrared vibrational spectroscopy (Dippy,1939; Allerhand and Schleyer, 1963; Krumm, Kurowa and Rebare, 1967; Green,1974; Jeng and Ault, 1991; Steinwender et al., 1993). Crystallographers, who formany years had a fixation on comparison with van der Waals radii, have been moreskeptical.

A survey of 113 neutron diffraction crystal structures by Taylor and Kennard (1982)favored the existence of C–H� � �O, C–H� � �N and C–H� � �Cl bonds with mean H� � �Odistances of 2.04 to 2.40 A, H� � �N 2.52 to 2.72 A, H� � �Cl 2.57 to 2.91 A. More recentlyDesiraju (1989, 1990, 1991) examined the C–H� � �O distances in crystal structurescontaining (Cl3�nCn) C–H� � �O, where 0 n 3, and in some alkyl and alkene struc-tures. The distances ranged from 3.0 to 4.0 A and decreased smoothly with increasingdonor group acidity. The more acidic the C–H, the shorter the C� � �O distance in thesequence alkyne>quinone>alkene>aromatic>aliphatic. Since C� � �O distancesalone are not reliable criteria for hydrogen-bonding, it is unfortunate that H� � �Obond lengths and C–H� � �O bond angles were not analyzed from those data wherethe hydrogen atoms were observed, or their positions could be calculated with reason-able certainty from those of the adjacent non-hydrogen atoms. Some examples of(CCl3) C–H� � �O hydrogen bond lengths � 2.5 A in crystal structures are reported byIrving and Irving (1992). The C–H� � �O distances in 551 crystal structures was shownto correlate with pK� (Me2SO) values, suggesting a new scale of carbon acidic(Pedireddi and Desiraju, 1992).

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A survey of C–H� � �O bonds in carbohydrate crystal structures only by Steiner andSaenger (1992c) was based on 30 neutron diffraction analyses providing 395 potentialdonors and 328 potential acceptors. All donors were Csp3–H; the acceptors wereC–OH (61%), C–O–C (27%), OwH2 (11%), O¼C or O¼C (1.5%). With a cut-off ofthe C–H� � �O angle greater than 90�, 5 percent have C–H� � �O contacts between 2.27and 2.4 A, 21 percent<2.5 A, 65 percent with contacts<2.7 A; if the cut-off isextended to 3.0 A, there are 93 percent contacts. More than half the contacts lessthan 2.7 A are intramolecular. Many have the configuration XXI or XXII, which is acharacteristic of syndiaxial interactions in carbohydrate molecules.

About 14 percent of the bonds>2.7 A are three-centered. This is smaller than the 25percent for O–H� � �O bonds in carbohydrates (Ceccarelli, Jeffrey and Taylor, 1981).

A subsequent survey of C–H� � �OH2 bonds based on 101 water molecules in 46 neu-tron diffraction crystal structure analyses by Steiner and Saenger (1993a) showed that 8percent of the water molecules had C–H� � �Ow, distances <2.5 A. For longer distances,the proportion increased to 39 percent <2.8 A and 57 percent<3.0 A.

Comparison with the analysis of the stereochemistry of water molecules in 311hydrates, amino acids, carbohydrates, purines and pyrimidines and nucleosides andnucleotides is given in Table IV. These data were mainly from X-ray analyses andC–H� � �Ow bonds were excluded (Jeffrey and Maluszynska, 1990). The difference inthe water donor percentages is likely to be a consequence of the difference in thedata sets used. The C–H� � �Ow analysis contained a number of salts and data from

TABLE IV Comparison (in percentages) of hydrogen-bond donor and acceptor properties of watermolecules, including C-H� � �Ow bonds from Steiner and Saenger (1993a) (S & S), and excluding C-H� � �Ow

bonds from from Jeffrey and Maluszynska (1990) (J & M)*

Water donors Water acceptors

S & S J & M S & S J & M

zero 0 6single 0 >1 single 17 43double 43 68 double 57 48triple 32 19 triple 21 3quadruple 22 12 quadruple 3 0quintupley 3 0 quintuplez 1 0

*H� � �A<3.0 A, C–H� � �A>90�, those involving metal cations were excluded.

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the neutron diffraction analyses of the cyclodextrin hydrates. The water acceptorpercentages show the expected trend towards higher levels of coordination whenC–H� � �Ow bonds are included. C–H� � �O single and bifurcated hydrogen bonds areobserved in the crystal structures of nucleosides and nucleotides with H� � �O distancesranging from 2.17 to 2.56 A. The C–H� � �O angles range from 170 to 90� (see Tables10.1 and 10.2 in Jeffrey and Saenger, 1991).

An examination of the high-resolution neutron diffraction of vitamin Bl2 co-enzyme(Bouquiere et al., 1993) for C–H� � �O interactions by Steiner and Saenger (1993b)found several examples of water molecules where the tetrahedral hydrogen-bond coor-dination is completed by C–H� � �Ow interactions. Crystal structures containing dimerslinked by C–H� � �O hydrogen bonds have been reported by Hariharan and Srinivasan(1990) and Jaulmes et al. (1993). In the crystal structure of 8-dimethylaminomethyl-l-dimethylammonio-methyl-naphthalene nitrate, the molecular packing is determinedchiefly by C–H� � �O� interactions to the nitrate oxygens with nine H� � �O� distancesfrom 2.31(1) to 2.57(2) A and C–H� � �O� angles of 144 to 171� (Salas, Kanters andGrech, 1992). A novel crystallographic way for testing for C–H� � �X hydrogen bondingis proposed by Steiner (1994). He examined the Ueq vibrational thermal motion par-ameters for the carbon atoms in 51 terminal Cð1Þ Cð2Þ�H groups in 42 crystal struc-tures. Plotting UeqC(2)/UeqC(1) he found that with H� � �X>3.0 A, the ratio was 1.4 orabove. With H� � �X<3.0 A, the ratio was below 1.4, with a rough correlation betweentheUeq ratio and the H� � �X distances. The implication is that hydrogen bonding reducesthe normal increase in thermal motion along these relatively rigid terminal groups.

Now that C–H hydrogen bonds have become fashionable again, crystallographerswill watch for them and no doubt many more will be reported.

7 HYDROGEN-BOND DISORDER; TUNNELLING; FLIP-FLOP; LOST BONDS

In strong symmetrical double minimum disordered hydrogen bonds such as

N–(H)� � �(H)–Nþ

, O�ðHÞ� � �ðHÞ� �OO, the proton crosses the potential energy barrierby tunnelling. This configurational change, i.e. bond breaking and making, has longbeen associated with characteristic intense infrared continua (Zundel, 1976, 1992;Eckert and Zundel, 1988). The proton polarizability of chains of such strong bondshas been described recently by Zundel and Brzezinski (1992), with application toproton jumping in bacteriorhodopsin (Olejnik, Brzezinski and Zundel, 1992). For theweaker uncharged –O–(H)� � �(H)–O– hydrogen bonds observed in the cyclodextrinhydrates, an alternative conformational mechanism has been proposed, known asflip-flop (Saenger et al., 1982; Betzel et al., 1984). This mechanism, XXIII, can alsobe applied to hydrogen bond disorder in the ices, where it involves a 120�

rotation about the oxygen atom, and where there is frequently an intermediateenergy minimum due to the formation of a three-center bond.

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The dynamics of the hydrogen-bonding disorder in �-cyclodextrin undecahydrate(�-CD-11H2O) was studied at room temperature by quasi-elastic incoherent neutronscattering by Steiner et al. (1989). The mean residence time of various different protonsis estimated to be � 0.6� 10�11 s. A later study by Steiner, Saenger and Lechner (1991)gives a more detailed description of the hydrogen-bond disorder in �-CD-11H2O and ofthe water molecules, some of which are guests in the cyclodextrin cavity. The quasi-elas-tic spectra were satisfactorily interpreted using a simple two-site jump model with reor-ientational jumps over H� � �H distances of � 1.5 A and diffusive motions of watermolecules in the cavity over H� � �H distances of � 3 A. The jump rates extend from� 2� 1010 to 2� 1011 s�1.

An example of multiple proton transfers in hydrogen-bonded dimers and trimers ofpyrazole derivatives in the solid state is observed with 15N NMR by Aquilas-Parrillaet al. (1992). The ices are a fertile field for studying hydrogen-bond disorder (Kamb,1968; Kuhs and Lehman, 1983). Powder neutron diffraction studies of the ices IIIand X by Londono, Kuhs and Finney (1993) show that the hydrogen atoms are notfully ordered in III and not quite symmetrically disordered in X.

In many of the carboxylic acid hydrogen-bonded dimers, the hydrogen atoms are dis-ordered (Dunitz and Strickler, 1968). Two mechanisms have been proposed; a doubleproton tunnelling (XXIV) or a dynamic double 180� flip (XXV) (Furic, 1984). Whilethe flip model might be energetically feasible in the gas phase, it seems veryunlikely in the solid state (Nagawa, 1984; Kanters et al., 1991a).

The interesting concept of lost hydrogen bonds in proteins is developed by Savageet al. (1993). The maximum hydrogen bond functionality for each amino acid residueis obtained by adding lone-pairs and hydrogen-bonding hydrogen atoms. Thenumber of observed hydrogen bonds based on O� � �O<3.4 A, N� � �N orN� � �O<3.5 A and N� � �S or O� � �S<3.8 A and angles >90� criteria is calculated for236 crystallographically independent protein molecules. For donors the number oflost bonds ranges from 5.7 percent for main chains to 0.3 for threonine. For acceptors,it is much larger, 34 percent for threonine (C–O) to 3 percent for glutamic acid (C–O).The excess of acceptor functionality over number of donor hydrogen atoms available isconsistent with the large number of three-center bonds reported by Preissner, Enger andSaenger (1991). There is an excellent linear correlation between the number of losthydrogen bonds (LHB) and the sum of the calculated stability factors for the proteins,as shown in Fig. 5.

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8 HYDROGEN BONDS IN INCLUSION COMPOUNDS

Since the crystal structure determination of the hydroquinone-SO2 complex by Palinand Powell (1947), and the urea n-hydrocarbon complex by Smith (1952), thenumber of inclusion compounds based on hydrogen-bond formation has steadilyincreased (Weber, 1987).*Water continues to be a source of new inclusion compounds.The air-hydrate has been found in deep-core ice. It is the 17A type II structurewith air occupying both the 12- and 16-hedra (Hondok et al., 1990). The 164 yearold mystery of the bromine clathrate hydrate (Lowing, 1829; Allen and Jeffrey, 1963)has been resolved by a single-crystal neutron diffraction analysis at 100K. The tetrago-nal crystal structure is a new type with a (H2O)n framework of 12-hedra, 14-hedra and15-hedra, with the Br2 molecules occupying the 14- and 15-hedra (Brammer andMcMullan, 1993).

FIGURE 5 Plot of number of lost hydrogen bonds, LHB, versus the sum of the stabilizing energy com-ponents. HP: hydrophobic energy; IP: ion pairs; SS: disulphide bonds.; Top for proteins better that 1.9 Aresolution. Bottom for proteins better than 1.7 A resolution. [from Savage et al. (1993), with permission.]

*A monograph by Sister Martinette Hagen (1962) gives an excellent review of the early days of clathrateinclusion compounds.

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A neutron diffraction analysis of the type II hydrate, 3.5Xe � 8CCl4 � 136D2O, at 13and 100K is reported by McMullan and Kvick (1990). The D� � �O hydrogen bondlengths range from 1.738 (3) to 1.802(1) A with O–D� � �O angles from 174.8(1) to180�. These are similar to the values from the neutron diffraction analysis of the typeI, 6C2H4O.46D2O, at 80K (Hollander and Jeffrey, 1977) where the D� � �O lengthsranged from 1.726 (2) to 1.815 (5) A with angles from 171.6(4) to 180�. Although theCCl4 molecules have the same point symmetry as the center of the 51262 polyhedrathat they occupy, they exhibit large amplitude 1ibration, with seven preferredorientations with C–Cl bonds directed towards the vertices of the polyhedron inwhich they are enclosed.

A neutron powder diffraction study of helium hydrate at 0.25GPa by Londono,Finney and Kuhs (1992) showed a gas hydrate with composition He � (6þ x)H2O thathas a host structure resembling that of ice II, space group R�33. A new clathrate hydrateof tetraisoamyl ammonium fluoride has been briefly reported. The alkyl chains ofthe cations are enclosed in 635742 polyhedra in a tetragonal I41/a structure(Lipkowski et al., 1990).

The polyhedral hydrates of the strong acids HPF6, HBF4 and HClO4 (Mootz, Oellersand Wiebcke, 1987) and of the strong base (CH3)4N �OH (Mootz and Seidel, 1990)provide a most interesting series of hydrogen-bonded water-ionic inclusion compounds.In the strong acid series, the host lattices are Hþ(H2O)n. They are isostructural with thetype I, cubic 12 A gas hydrates despite an extra proton.

The structure of the low-temperature, � tetramethyl ammonium hydroxide 5H2Owas determined by McMullan, Mak and Jeffrey (1966) in which the cage is a brokentruncated octahedron.

Mootz and Seidel (1990), Mootz and Staben (1992) have now characterized the wholephase diagram and analyzed the crystal structures of twelve hydrates: � and � 2H2O; �and � 4H2O; � and � 4.6H2O; � 5H2O; 6.67H2O; � and � 7.5H2O; 8. 75H2O; 10H2O.

The � and � forms of the dihydrate have one-dimensional ðH �OOðHOHÞ4 chains withone OH� proton not participating. The tetrahydrates have deprotonated waterchannels with O–H� � �Ow bonds. The 4.6�, 5�, 6.67, 7.5� hydrates form incompletepolyhedral cages with some oxygens three-coordinated. The high temperature �7.5,and the 8.75 and 10 hydrates are true clathrates with complete four-connectedð �OOH:nH2OÞ cages. The �7.5 hydrate has the 15-hedron [51263] and a vacant [4258]decahedra. The 10-hydrate has two new cages, a 17-hedra [4151066] and a vacantnonahedron [4366].

A most interesting structure of Cs{(CH3)4N}2(OH)3 � 14H2O has recently beenreported by Mootz and Staben (1994). It is isostructural with the (CH4)4N �OH.7.5hydrate with the Csþ ions occupying the small monohedra. In contrast to the hydratesof the strong acids, which have an extra proton, these host lattices are proton deficient.In both cases, proton excess and proton deficiency result in disorder, but the details ofhow the proton distribution in the bonds adjusts to the excess or deficiency are notclear. The capability of forming hydrogen-bond water lattices with an excess ordeficiency of protons is an interesting feature of clathrate hydration which meritsfurther study by careful neutron diffraction analyses.

The channel type of hydrate inclusion compounds, of which (CH3)4NOH � 4H2O is anexample, is a common form of inclusion hydrate in which the water-anion layers arecomposed of fused polyhedra including quadrilaterals, pentagons, hexagons andheptagons, as shown in Table V. The recent additions are [12CH3N]þ[12F � 28H2O]�

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with quadrilaterals and hexagons, [CH3N]þ[F � 5H2O]� with pentagons only (Stabenand Mootz, 1993), CH3COH � 2H2O with pentagons only, and CH3COH � 7H2O withquadrilaterals, pentagons and hexagons (Mootz and Staben, 1993).

There is a brief report of a hydrate of tetrapropyl ammonium fluoride with water-fluoride layers containing fused quadrilaterals, pentagons and hexagons with thelayer interspersed by the propyl groups (Lipkowski et al., 1992). Hydrogen-bondedchannel clathrate structures of 1,2-naphthalene dicarboxylic acid which include avariety of organic solvents or water are described by Fitzgerald, Gallucci and Gerkin(1992). The diacetylenic diols form crystalline inclusion complexes which are used forcommercial extraction processes (Toda, 1987). The crystal structure of one of theseclathrates with dichloromethane as the guest species is reported by Leigh, Moodyand Pritchard (1994). The host lattice is an unusual tubular structure with double-walled channels formed by infinite columns of O–H� � �O hydrogen bonds.

Fused polyhedra were observed in a drug-deoxydinucleotide phosphate complex byNeidle et al. (1980). A recent high-resolution neutron diffraction refinement of vitaminB12 coenzyme showed fused quadrilaterals and pentagons in the hydrogen-bondedwater network with O� � �O distances between 2.61 and 3.03 A at 15 K (Bouquiereet al., 1993).

The crystal structure at � 80�C of a dodecahydrate of the oligopeptide cyclic D-valyl-(N2-methyl-L-arginyl)-glycyl-L-aspartyl-3-(aminomethyl)-benzoic acid 12H2O (27.3percent water by weight) has recently been reported (Harlow, 1993). The water mol-ecules form a semi-clathrate-like structure with a 4- and several 5-, 6- and 7-memberedrings. This water structure is hydrogen-bonded at several points to the peptidemolecule.

Since proteins in the crystalline state are completely surrounded by bound water,these crystal structures could be regarded as semi-clathrate hydrates. Only in the caseof the small plant protein, crambin, have polyhedral arrangements of hydrogenbonds been identified (Teeter and Whitlow, 1987). The problem of identifyinghydrogen-bond motifs in the hydration of proteins lies in the inability to distinguishhydrogen-bonded and non-bonded O� � �O separations from O� � �O distances alone(see Fig. 2), particularly when disorder is likely to be present. Fascinatingsuper-diamond host lattices are formed by pair-wise hydrogen bonding between theCOOH groups in 2,6-dimethylidine adamantane 1,3,5,7-tetracarboxylic acids (Ermer,

TABLE V Channel- and layer-type inclusion hydrates with hydrogen-bonded layers of fused quadrilaterals(Q), pentagons (P), hexagons (H6) and heptagons (H7).

Compound Layer topology Reference

[(CH3)4N]þ[F � 4H2O]� H6 McLean and Jeffrey (1967)[(CH3)4N]2

þ[SO4 � 4H2O]�2 H6 McLean and Jeffrey (1968)[(C2H5)4N]þ [Cl � 4H2O]� Q, H6 Mak, Bruinslot and Beurskens (1986)[4(H2H5)4N]þ[F � 11H2O]� Q Mak (1985)[(C2H5)4n]

þ[CH3COO � 4H2O]� P, H7 Mak (2985)Pyridine 3H2O Q, P, H6 Mootz and Wussow (1981)Pinacol 6H2O P Kim and Jeffrey (1970)Piperazine 6H2O P Schwarzenbach (1968)2,5-dimethyl 2,5-hexanediol 4H2O P Jeffrey and Shen (1972)2,5-dimethyl 2,5-octanediol 4H2O P Jeffrey and Mastropaolo (1978)[C12H28N]þ[F � 11H2O]� Q, P, H Lipkowski et al. (1992)

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1988). Five more crystal structures of this type are reported by Ermer and Lindenberg(1991).

In the phenol-formaldehyde oligomer inclusion compounds, the calixarenes, thephenolic components are linked by covalent bonds (Andretti and Ugozzoli, 1991).The phenolic O–H bond can be unsubstituted or substituted. A four-memberedhomodromic ring of strong O–H� � �O bonds influences the conformation of thecalixarene, forcing a cone-conformation which is not present when the hydroxylgroups are partially or wholly substituted. Bavoux and Perrin (1992) report aO–H� � �N � (C2H6)3 hydrogen bond with O� � �N distance of 2.632 (8) A in the crystalstructure of p-t-butyl-dihomooxa-calix [4] arene: triethylamine (1 : 2) clathrate.

Some of the oldest known inclusion compounds are those of the cholic acids. Thecrystal structures of the 1 : 1 inclusion compounds of cholic acid with methanol, ethanoland 1-propanol have been studied by Jones and Nassimbeni (1990). The moleculeswhich form the cage are linked by hydrogen bonds with O� � �O separations from 2.55to 2.85 A; the hydrogen bond lengths and angles were not reported.

Hydrogen-bonded cyclamers of 1,3-cyclohexanedione have been reported by Etterel al. (1990). These form hexameric rings which enclose benzene. A clathrate-typehost lattice is formed by hydrogen-bonded molecules of 9-benzamido-6, 7, 8, 9, 10, 11-hexahydro-5, 9, 7, 11-dimethano-5H-benzocyclonen-7-o1 (XXVI) through the forma-tion of O–H� � �O¼C and N–H� � �O–H bonds. The guest species are carbon tetrachlorideor ethyl acetate (Bishop et al., 1991).

9 X–H� � � p BONDS

The concept of NH � � �� hydrogen bonding is a tempting concept which has been sug-gested in protein structures (Burley and Petsko, 1985; Levitt and Perutz, 1988). A

search for the most favorable scenario, O–H� � � jjjC

C, yielded only one example, the crystal

structure of 2-ethyladamantin-2-ol, which revealed a cyclic dimer motif with C–H–�bond lengths of 2.22 A (Steinwendet et al., 1993). O-H� � �� hydrogen bonding toaromatic rings has been reported in crystal structures by Hardy and MacNicol(1976), Atwood et al. (1991, 1992) and Ferguson et al. (1994), with H� � �Carom distancesfrom 2.1 to 2.7 A. The role of C–H� � �� hydrogen bonds in stabilizing cyclophane host-guest complexes in organic solutions is discussed by Cochran et al. (1992).

Crystalline complexes of 2-butyne-HCl and 2-butyne-2HCl, decomposing at � 100�Cand melting at � 113�C respectively, were identified and the crystal structures were

determined by Mootz and Deeg (1992), showing Cl–H� � �jjjC

Cwith H� � � jjj bonds of

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2.30 A and Cl–H� � � jjj angles of 180� and 165�. Deeg and Mootz (1993) have also deter-mined the crystal structures of toluene-2HCl and mesitylene-HCl. The HCImolecules are located on both sides and one side respectively of the benzene rings,with the Cl–H bonds pointing to the center and nearly perpendicular to the benzenerings, as shown in Fig. 6. The H� � ��(center) distances are 2.51 (8) and 2.32(5) A.Recent vibrational spectroscopic evidence for O–H� � �� has been provided bySteinwender et al. (1993). There is little doubt that this is a weak hydrogen-bond-interaction (as defined by Pimental and McClellan, 1960, p. 6) which is observedwhen the other stronger intermolecular forces allow a C–H bond to be directed normaland towards the center of a CC bond or an aromatic ring.

FIGURE 6 The toluene � 2HCl hydrogen-bonded complex, ORTEP at 25% probability. [from Deeg andMootz (1992), with permission.]

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10 MOLECULAR RECOGNITION AND HYDROGEN BONDING

Molecular recognition is one of the buzz-words* of the 1990s. Presumably it is a processwhereby molecules self-assemble to form crystals with the reduction of thermal motionor the evaporation of solvent. However, this mundane process is not what attractsattention; rather it is heterogeneous molecular recognition. This is a process that resultsin complex formation, co-crystallization and the adherence of substrates to enzymes,so-called supra-molecular chemistry. The concept is defined by a definitive article byRebek (1988) who described molecular recognition as a process at the foundation of thecurrent revolution in molecular biology and technology. A glance at the illustrativeexamples in this article shows that hydrogen bonding frequently plays a key role. Therecognition of hydrogen-bonding motifs or nets by graph theory may permit the iden-tification of possible substrates to the known structure of proteins and nucleic acids.

It can lead to the synthesis of crystals with special properties (Etter, 1990) and thedesign of host systems for small biological molecules, including drugs (Rebek, 1990)and the formation of supramolecular assemblies (e.g. Seto and Whitesides, 1991;Chang et al., 1991; Kikuchi et al., 1991). Crystallography can play a key role inmolecular recognition, not only in providing the known structure of the macromole-cules, but also as a means of identifying potential complexing molecules by searchesusing the Cambridge Crystallographic Data Base.

The related concept of using hydrogen-bond interactions to form aggregatestructures with predictable connectivities and symmetry developed from, or wasresponsible for, the graph theory approach of Etter discussed earlier.

In the biological field, molecular recognition generally takes place through anaqueous medium, and hydrogen-bonding will certainly play a role (cf. Kurihara et al.,1991). It has been suggested that electron or proton polarizability through the transientcooperative hydrogen-bonded chains in the water motifs provides a mechanismfor molecular recognition prior to actual intermolecular contact, i.e. Nature’s radarguidance system (Zundel, 1992; Zundel and Brzezinski, 1992; Jeffrey, 1993, 1994).

11 MISCELLANEOUS

A configuration change on deuteration. Mootz and Schilling (1992) observed aunique structural change in the crystal structure of trifluoroacetic acid tetrahydrate (mp� 12�C) on deuteration. The hydrogenated phase is ionic [H5O2]

þ[(CHCOO)2H]� �

6H2O, while the deuterated phase (mp � 15�C) is molecular CF3COOD � 4H2O. Thetopologies of the two structures are very similar, with buckled layers of water moleculesconsisting of condensed four- and six-membered rings of O–H(D)� � �O hydrogen bonds.The difference lies in the distribution of the hydrogen and deuterium atoms. In theH2O structure, the four-membered rings are homodromic, one six-membered ring ishomodromic and the other heterodromic. In the D2O structure, the four-memberedrings are heterodromic and both six-membered rings are homodromic. The shortesthydrogen bonds are C–O–D� � �OD2, 1.60(2) A, and C–O–(H)� � �(H)–O� � � �CC, 1.65(4) A,which is symmetrically disordered.

*A buzz-word is a word that is added to the title or abstract of a paper or a grant proposal in order toenhance the chances of (a) an oral presentation, (b) an accepted publication, or (c) a funded research grant.

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Liquid-crystal mesogens. The crystal structures of the 36 glyco-lipids carried outfrom the 1965 to 1992 have recently been summarized by Pascher et al. (1992). Inthese crystals the glycosidic head groups are linked by networks of hydrogen bondswhich interface with water molecules in the lyotropic liquid crystal phases.

The more recent interest in non-biological carbohydrate-based liquid crystals formedby alkyl substitution (CnH2nþ 1 with n>6) of cyclic and acyclic monosaccharides(Jeffrey, 1986) has resulted in crystal structure analyses of seven n-alkyl pyranosidesand eight acyclic aldonamides and amido-alditols (Jeffrey and Wingert, 1992). Inthese crystal structures, the carbohydrate head-groups are hydrogen-bonded to formbilayers with interdigitizing alkyl chains. An exception is a group of structures withmonolayer head-to-tail packing. These structures which have three different spacegroups have a similar hydrogen-bonding motif. This motif includes a homodromicquadrilateral of O–H� � �O bonds. On heating, the crystal structures transform to abilayer head-to-head packing prior to forming a bilayer (smectic) liquid crystal.It is proposed that the homodromic cyclic pattern of bonds stabilizes the unusualhead-to-tail packing (Jeffrey, 1990). The same type of homodromic quadrilateralof hydrogen bonds is observed in the crystal structures of alditol derivatives and is pos-tulated to play a significant role in the molecular packing (Andre et al., 1993). The moresoluble of these compounds, such as n-octyl, �-glucopyranoside, form lyotropic liquidcrystals in which the hydrogen-bonded carbohydrate moieties interface with the watermolecules (Chung and Jeffrey, 1989).

Apologies

As with all reviews, this article reflects the interests of the author. The present-day ever-increasing multiplicity of publications, authors and journals makes it almost impossibleto cover all aspects of a complex field. Apologies are offered to those whose favoritepublication has been omitted.

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SUBJECT INDEX

acetic acid 144

alditol derivatives 165

aldonamides 165

amido-alditols 165

amino acids 138, 156, 158

aminobutyric acid 140

asparagine monohydrate 141

bacteriorhodopsin 157

barbiturates 148

bifurcated 137

bond angle 136, 144, 148

bond-length 136

bromine clathrate hydrate 159

butyne-HCl 162

calixarenes 141, 162

carbohydrates 138, 140, 142, 143, 144, 145,

146

carbohydrate hydrates 143

carboxylic acids 140, 150

caronic acids 150

CHARMM 142

cholic acids 162

clathrate hydrates 143

conic correction 136

cooperativity 142, 144

crambin 161

cyclic water polymers 144

cyclodextrin 138, 144, 147

cyclodextrin deuterate 138

cyclodextrin-ethanol-octahydrate 138

cyclodextrin hydrates 144, 157

cyclodextrin undecahydrate 158

cyclohexanedione 162

cyclophane 162

deoxydinucleotide phosphate complex

161

deuteration 148, 164

diacetylenic diols 161

diamines 152

diketones 145

diketo-enols 150

dimethylamine fluorine 152

dimethylamine naphthalene 152

dimethylamine phenanthrine 152

dimethylaminomethyl-dimethylammonio-

methyl-naphthalene nitrate 157

dimethylidine adamantane

tetracarboxylic acids 161

DNA 138

drugs 164

ethyladamentinol 162

excluded region 136

flip-flop 157

formamide 140, 144

formic acid 144

glucopyranose 142

glutamic acid 158

glycine 137

glyco-lipids 165

graph theory 143

GROMOS 142

helium hydrate 160

Hsquarate 152

hydrogen-bond structure 142

hydrogen diquinuclidinone 153

hydroquinone-SO2 complex 159

ice, ices 136, 142, 143, 145, 157, 158, 159

imidazolium maleate 150

inclusion compounds 159

KF � (CH2COOH)2 141

lactulose 140

liquid-crystal mesogens 165

lost hydrogen bonds 157

lower-bound model 148

malonaldehyde 145

mesitylene-HCl 163

methyl-glucopyranoside 141

molecular mechanics program 141

molecular recognition 164

monosaccharides 144, 145

motif 142

neutron diffraction 138

nucleic acids 142, 145, 164

nucleosides 138, 148

nucleotides 138, 142, 148

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oligopeptide 161

oxalic acid acetamide 140

oxalic acid dihydrate 140

oximes 144

oxyacids 146

pentachlorophenol 151

phthalazine methyl tetraazothionate 153

phthalazine semi-tetrafluoroborate 152

polypeptide bond 148

potassium hydrogen chloromaleate 150

propronic acid 144

protein crystal structures 138, 147

proteins 142, 145, 158

proton polarizability 157

proton sponges 150

purines 138, 148, 156

pyrimidines 138, 148, 156

pyranosides 165

pyrazole derivatives 158

resonance assisted hydrogen bonding

(RAHB) 143, 144, 145, 151

riding-motion model 148

strong acids 160

strong base 160

tetraethylammonium fluoride

hydrates 141

tetraisoamyl ammonium fluoride 160

tetramethyl ammonium hydroxide 160

tetrapropyl ammonium fluoride 161

three-centered 137

threonine 158

toluene-2HCl 163

trifluoroacetic acid tetrahydrate 164

urea hydrocarbon complex 159

vitamin B12 co-enzyme 157, 161

water 136, 141, 142, 143, 144, 156

zwitterionic amino acids 138

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