The whole palette of hydrogen bonds

1. Introduction

The hydrogen bond was discovered almost 100 years ago,[1]

but still is a topic of vital scientific research. The reason forthis long-lasting interest lies in the eminent importance ofhydrogen bonds for the structure, function, and dynamics of avast number of chemical systems, which range from inorganicto biological chemistry. The scientific branches involved arevery diverse, and one may include mineralogy, materialscience, general inorganic and organic chemistry, supramo-lecular chemistry, biochemistry, molecular medicine, andpharmacy. The ongoing developments in all these fields keepresearch into hydrogen bonds developing in parallel. In recentyears in particular, hydrogen-bond research has stronglyexpanded in depth as well as in breadth, new concepts havebeen established, and the complexity of the phenomenaconsidered has increased dramatically. This review is intendedto give a coherent survey of the state of the art, with a focus on

the structure in the solid state, and with weight put mainly onthe fundamental aspects. Numerous books[29] and reviews onthe subject have appeared earlier, so a historical outline is notnecessary. Much of the published numerical material issomewhat outdated and, therefore, this review contains somenumerical data that have been newly retrieved from the mostrelevant structural database, the Cambridge Structural Data-base (CSD).[10]

It is pertinent to recall here the earlier classical view onhydrogen bonding. One may consider the directional inter-action between water molecules as the prototype of allhydrogen bonds (Scheme 1, definitionsof geometric parameters are also in-cluded). The large difference in electro-negativity between the H and O atomsmakes the OH bonds of a watermolecule inherently polar, with partialatomic charges of around 0.4 on eachH atom and 0.8 on the O atom.Neighboring water molecules orient insuch a way that local dipoles OHpoint at negative partial charges O,that is, at the electron lone pairs ofthe filled p orbitals. In the resulting

The Hydrogen Bond in the Solid State

Thomas Steiner*

In memory of Jan Kroon

The hydrogen bond is the most impor-tant of all directional intermolecularinteractions. It is operative in deter-mining molecular conformation, mo-lecular aggregation, and the functionof a vast number of chemical systemsranging from inorganic to biological.Research into hydrogen bonds experi-enced a stagnant period in the 1980s,but re-opened around 1990, and hasbeen in rapid development since then.In terms of modern concepts, the hy-drogen bond is understood as a verybroad phenomenon, and it is acceptedthat there are open borders to other

effects. There are dozens of differenttypes of XH A hydrogen bondsthat occur commonly in the condensedphases, and in addition there are in-numerable less common ones. Dissoci-ation energies span more than twoorders of magnitude (about 0.2 40 kcalmol1). Within this range, thenature of the interaction is not con-stant, but its electrostatic, covalent,and dispersion contributions vary intheir relative weights. The hydrogenbond has broad transition regions thatmerge continuously with the covalentbond, the van der Waals interaction,

the ionic interaction, and also thecation interaction. All hydrogenbonds can be considered as incipientproton transfer reactions, and forstrong hydrogen bonds, this reactioncan be in a very advanced state. In thisreview, a coherent survey is given on allthese matters.

Keywords: donor acceptor systems electrostatic interactions hydrogenbonds noncovalent interactions proton transfer

[*] Dr. T. SteinerInstitut fr ChemieKristallographieFreie Universitt BerlinTakustrasse 6, 14195 Berlin (Germany)Fax: (49)30-838-56702E-mail : steiner@chemie.fu-berlin.de

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Scheme 1. Prototypeof a hydrogen bond:the water dimer. Def-initions of geometri-cal parameters: dH O distance, DO O distance, OH O angle.

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OH O interaction, the intermolecular distance is short-ened by around 1 compared to the sum of the van der Waalsradii for the H and O atoms[11] (1 100 pm), which indicatesthere is substantial overlap of electron orbitals to form athree-center four-electron bond. Despite significant chargetransfer in the hydrogen bond, the total interaction isdominantly electrostatic, which leads to pronounced flexibil-ity in the bond length and angle. The dissociation energy isaround 3 5 kcalmol1.This brief outline of the hydrogen bond between water

molecules can be extended, with only minor modifications, toanalogous interactions XH A formed by strongly polargroups XH on one side, and atoms A on the other(XO, N, halogen; AO, N, S, halide, etc.). Many aspects ofhydrogen bonds in structural chemistry and structural biologycan be readily explained at this level, and it is certainly therelative success of these views that made them dominate theperception of the hydrogen bond for decades. This dominancehas been so strong in some periods that research on hydrogenbonds differing too much from the one between watermolecules was effectively impeded.[8]

Today, it is known that the hydrogen bond is a muchbroader phenomenon than sketched above. What can becalled the classical hydrogen bond is just one amongmanya very abundant and important one, though. We knowof hydrogen bonds that are so strong that they resemblecovalent bonds in most of their properties, and we know ofothers that are so weak that they can hardly be distinguishedfrom van der Waals interactions. In fact, the phenomenon hascontinuous transition regions to such different effects as thecovalent bond, the purely ionic, the cation , and thevan der Waals interaction. The electrostatic dominance ofthe hydrogen bond is true only for some of the occurringconfigurations, whereas for others it is not. The H Adistance is not in all hydrogen bonds shorter than the sum ofthe van der Waals radii. For an XH group to be able to formhydrogen bonds, X does not need to be very electroneg-ative, it is only necessary that XH is at least slightly polar.This requirement includes groups such as CH, PH, andsome metal hydrides. XH groups of reverse polarity,XH, can form directional interactions that parallelhydrogen bonds (but one can argue that they should not becalled so). Also, the counterpart A does not need to be a

particularly electronegative atom or an anion, but only has tosupply a sterically accessible concentration of negative charge.The energy range for dissociation of hydrogen bonds coversmore than two factors of ten, about 0.2 to 40 kcalmol1, andthe possible functions of a particular type of hydrogen bonddepend on its location on this scale. These issues shall all bediscussed in the following sections.For space reasons, it will not be possible to cover all aspects

of hydrogen bonding equally well. Therefore, some importantfields, for which recent guiding reviews are available, will notbe discussed in great length. One example is the role ofhydrogen bonds in molecular recognition patters (supra-molecular synthons),[12] and the use of suitably robust motifsfor the construction of crystalline archtitectures with desiredproperties (crystal engineering).[13, 14] This area includes theinterplay of hydrogen bonds with other intermolecular forces,with whole arrays of such forces, and hierarchies within suchan interplay. The reader interested in this complex field isreferred to the articles of Desiraju,[12, 13] Leiserowitz et al.,[15]

and others.[16] A further topic which could not be covered hereis the symbolic description of hydrogen bond networks usingtools of graph theory,[17] in particular the graph set analy-sis.[18] An excellent guiding review is also available in thiscase.[19] For hydrogen bonding in biological structures, theinterested reader is referred to the book of Jeffrey andSaenger,[5] and for theoretical aspects to the book ofScheiner[7] as well as other recent reviews.[20] Results obtainedwith experimental methods other than diffraction will betouched upon only briefly, and will possibly leave somereaders dissatisfied. The role of hydrogen bonding in specialsystems will not be discussed at all, simply because there aretoo many of them.

2. Fundamentals

2.1. Definition of the Hydrogen Bond

Before discussing the hydrogen bond itself, the matter ofhydrogen bond definitions must be addressed. This is animportant point, because definitions of terms often limitentire fields. It is, also, a problematic point because verydifferent hydrogen bond definitions have been made, and part

50 Angew. Chem. Int. Ed. 2002, 41, 48 76

Thomas Steiner, born in 1961 near Reutte/Tirol in Austria, studied experimental physics at theTechnical University Graz, and obtained his Ph.D. in 1990 at the Freie Universitt Berlin withProf. Wolfram Saenger. He completed his habilitation in 1996, also at the Freie UniversittBerlin (Faculty of Chemistry). He was guest scientist with Prof. Jan Kroon at the BijvoetCenter for Biomolecular Research at Utrecht University, The Netherlands in 1995, and withProf. Joel L. Sussman at the Department of Structural Biology at the Weizmann Institute ofScience, Israel in 1997/8. His research interests are hydrogen bonds and other intermolecularinteractions in structural chemistry and biology. The methods used for investigation are neutronand X-ray diffraction, neutron scattering, crystal engineering, IR spectroscopy, databaseanalysis, and crystal correlation. The systems studied range from organic (terminal alkynes,binary proton transfer complexes) and bioorganic (peptides, steroids) to biological (proteins).Together with Prof. G. R. Desiraju, he is an author of a book on weak hydrogen bonds.

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of the literature relies quite uncritically on the validity (or thevalue) of the particular definition that is adhered to.Time has shown that only very general and flexible

definitions of the term hydrogen bond can do justice tothe complexity and chemical variability of the observedphenomena, and include the strongest as well as the weakestspecies of the family, and inter- as well as intramolecularinteractions. A far-sighted early definition is that of Pimenteland McClellan, who essentially wrote that ...a hydrogenbond exists if 1) there is evidence of a bond, and 2) there isevidence that this bond sterically involves a hydrogen atomalready bonded to another atom.[2] This definition leaves thechemical nature of the participants, including their polaritiesand net charges, unspecified. No restriction is made on theinteraction geometry except that the hydrogen atom must besomehow involved. The crucial requirement is the existenceof a bond, which is itself not easy to define. The methods totest experimentally if requirements 1 and 2 are fulfilled arelimited. For crystalline compounds, it is easy to see withdiffraction experiments whether an H atom is involved, but itis difficult to guarantee that a given contact is actuallybonding.A drawback of the Pimentel and McClellan definition is

that in the strict sense it includes pure van der Waals contacts(which can be clearly bonding, with energies of severaltenths of a kcalmol1), and it also includes three-center two-electron interactions where electrons of an XH bond aredonated sideways to an electron-deficient center (agosticinteraction). From a modern viewpoint, it seems advisable tomodify point 2, such as by requiring that XH acts as a proton(not electron) donor. Therefore, the following definition isproposed:

An XH A interaction is called a hydrogen bond, if1. it constitutes a local bond, and 2. XH acts as protondonor to A.

The second requirement is related to the acid/base proper-ties of XH and A, and has the chemical implication that ahydrogen bond can at least in principle be understood as anincipient proton-transfer reaction fromXH toA. It excludes,for example, pure van der Waals contacts, agostic interactions,so-called inverse hydrogen bonds (see Section 8), andB-H-B bridges. As a matter of fact, point 2 should beinterpreted liberally enough to include symmetric hydrogenbonds XHX, where donor and acceptor cannot be distin-guished. The direction of formal or real electron transferin a hydrogen bond is reverse to the direction of protondonation.Apart from general chemical definitions, there are many

specialized definitions of hydrogen bonds that are based oncertain sets of properties that can be studied with a particulartechnique. For example, hydrogen bonds have been definedon the basis of interaction geometries in crystal structures(short distances, fairly linear angles ), certain effects in IRabsorption spectra (red-shift and intensification of XH, etc.),or certain properties of experimental electron density distri-butions (existence of a bond critical point between H andA, with numerical parameters within certain ranges). All suchdefinitions are closely tied to a specific technique, and may be

quite useful in the regime accessible to it. Nevertheless, theyare more or less useless outside that regime, and many amisunderstanding in the hydrogen bond literature has beencaused by applying such definitions outside their region ofapplicability.The practical scientist often requires a technical definition,

and automated data treatment procedures for identifyinghydrogen bonds cannot be done without. It is not within thescope of this article to discuss any set of threshold values thata hydrogen bond must pass in any particular type oftechnical definition. It is only mentioned that the van derWaals cutoff definition[21] for identifying hydrogen bonds ona structural basis (requiring that the H A distance issubstantially shorter than the sum of the van der Waals radiiof H and A) is far too restrictive and should no longer beapplied.[5, 6, 8] If distance cutoff limits must be used, XH Ainteractions with H A distances up to 3.0 or even 3.2 should be considered as potentially hydrogen bonding.[6] Anangular cutoff can be set at 90 or, somewhat moreconservatively, at 110. A necessary geometric criterionfor hydrogen bonding is a positive directionality preference,that is, linear XH A angles must be statistically favoredover bent ones (this is a consequence of point 2 of the abovedefinition).[22]

2.2. Further Terminology

A large part of the terminology concerning hydrogen bondsis not uniformly used in the literature, and still today,terminological discrepancies lead to misunderstanding be-tween different authors. Therefore, some of the technicalterms used in this review need to be explicitly defined.In a hydrogen bond XH A, the group XH is called the

donor and A is called the acceptor (short for proton donorand proton acceptor, respectively). Some authors prefer thereverse nomenclature (XH electron acceptor, Y electrondonor), which is equally justified.In a simple hydrogen bond, the

donor interacts with one acceptor(Scheme 2a). Since the hydro-gen bond has a long range, adonor can interact with two andthree acceptors simultaneously(Scheme 2b, c). Hydrogen bondswith more than three acceptorsare possible in principle, but areonly rarely found in practice be-cause they require very highspatial densities of acceptors.The terms bifurcated and tri-furcated are commonly used todescribe the arrangements inScheme 2b and c, respectively.The term two-centered hydro-gen bond is an alternative descrip-tor for XH A (Scheme 2a)where the H-atom is bonded totwo other atoms, and is itself not

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X H A

X HA

X H A

A

A

A

b)

c)

a) d

d1

d2

d1d2

d3

Scheme 2. Different typesof hydrogen bridges. a) Nor-mal hydrogen bond with oneacceptor. b) Bifurcated hy-drogen bond; if the twoH A separations are dis-tinctly different, the shorterinteraction is called majorcomponent, and the longerone the minor component ofthe bifurcated bond. c) Tri-furcated hydrogen bond.

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counted as a center. Consequently, the arrangements inScheme 2b and 2c may be called three- and four-centered hydrogen bonds, respectively.[5, 6] This terminologyis logical, but leads to confusion from the point of view ofregarding hydrogen bonds OH O as three-center four-electron interactions, where the H-atom is counted as acenter. A bifurcated hydrogen bond (Scheme 2b) is thentermed three-centered, but also represents a four-centersix-electron interaction. To avoid such ambiguities, the olderterm bifurcated is used here.There is particular confusion concerning the terms attrac-

tive and repulsive. Some authors use these terms to character-ize forces, and others to characterize energies. In the lattercase, an attractive interaction is taken as a synonym forbonding interaction, that is, one that requires the input ofenergy to be broken. Following well-founded recommenda-tions,[23] the terms attractive and repulsive are used hereexclusively to describe forces. Negative and positive bondenergies are indicated by the terms stabilizing (or bond-ing) and destabilizing, respectively. The schematic hydro-gen bond potential in Figure 1 shows that a stabilizinginteraction (that is, with E 0) is associated with a repulsiveforce if it is shorter than the equilibrium distance (see figurelegend for further details).[8]

Figure 1. Schematic representation of a typical hydrogen bond potential.[8]

A hydrogen bond length differing from d0 implies a force towards ageometry of lower energy, that is, by attraction if dd0 and repulsion if dd0 . Note that the interaction can at the same time be stabilizing (orbonding) and repulsive! The distortions from d0 occurring in practiceare limited by the energy penalties that have to be paid, and in crystals, onlya few hydrogen bonds have energies differing by more than 1 kcalmol1

from optimum.

Hydrogen bonds are sometimes called nonbonded inter-actions. At least to this author, this appears a contradiction interms which should be avoided.

2.3. Constituent Interactions

The hydrogen bond is a complex interaction composed ofseveral constituents that are different in their natures.[6, 7]

Most popular are partitioning modes that essentially followthose used by Morokuma.[24] The total energy of a hydrogenbond (Etot) is split into contributions from electrostatics (Eel),

polarization (Epol), charge transfer (Ect), dispersion (Edisp), andexchange repulsion (Eer), somewhat different, but still related,partitioning schemes are also in use. The distance andangular characteristics of these constituents are very different.The electrostatic term is directional and of long range(diminishing only slowly as r3 for dipole dipole and as r2 for dipole monopole interactions). Polarization de-creases faster ( r4) and the charge-transfer term decreaseseven faster, approximately following er. According to naturalbond orbital analysis,[25] charge transfer occurs from anelectron lone pair of A to an antibonding orbital of XH,that is nA*XH. The dispersion term is isotropic with adistance dependence of r6. The exchange repulsion termincreases sharply with reducing distance (as r12). Thedispersion and exchange repulsion terms are often combinedinto an isotropic van der Waals contribution that is approx-imately described by the well-known Lennard Jones poten-tial (EvdWA r12B r6). Depending on the particular chem-ical donor acceptor combination, and the details of thecontact geometry, all these terms contribute with differentweights. It cannot be globally stated that the hydrogen bond assuch is dominated by this or that term in any case.Some general conclusions can be drawn from the overall

distance characteristics. In particular, it is important that of allthe constituents, the electrostatic contribution reduces slowestwith increasing distance. The hydrogen bond potential for anyparticular donor acceptor combination (Figure 1) is, there-fore, dominated by electrostatics at long distances, even ifcharge transfer plays an important role at optimal geometry.Elongation of a hydrogen bond from optimal geometry alwaysmakes it more electrostatic in nature.In normal hydrogen bonds Eel is the largest term, but a

certain charge-transfer contribution is also present. Thevan der Waals terms too are always present, and for theweakest kinds of hydrogen bonds dispersion may contributeas much as electrostatics to the total bond energy. Purelyelectrostatic plus van der Waals models can be quitesuccessful despite their simplicity for hydrogen bonds ofweak to intermediate strengths.[26] Such simple models fail forthe strongest types of hydrogen bonds, for which their quasi-covalent nature has to be fully considered (see Section 7).

2.4. Energies

The energy of hydrogen bonds in the solid state cannot bedirectly measured, and this circumstance leaves open ques-tions in many structural studies. Computational chemistry, onthe other hand, produces results on hydrogen bond energies atan inflationary rate,[7, 20] many obtained at high levels of theoryand even more in rather routine calculations using black-boxmethods. Theoretical studies are not the topic of the presentreview, but an idea of typical results can be gained from thecollection of calculated values listed in Table 1.[27] It appearsthat hydrogen bond energies cover more than two orders ofmagnitude, about 0.2 to 40 kcalmol1. On a logarithmicscale, the bond energy of the water dimer is roughly in themiddle.

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The values in Table 1 are computed for dimers in optimalgeometry undisturbed by their surroundings. In the solid state,hydrogen bonds are practically never in optimal geometry,and are always influenced by their environment. There arenumerous effects from the close and also from the remotesurrounding that may considerably increase or lower hydro-gen bond energies (crystal-field effects). Hydrogen bondsdo not normally occur as isolated entities but form networks.Within these networks, hydrogen bond energies are notadditive (see Section 4). In such cases, it is not reasonable tosplit up the network into individual hydrogen bonds and tocalculate energies for each one. In this sense, calculatedhydrogen bond energies should always be taken with caution.

2.5. Transition to Other Interaction Types

As outlined previously, the hydrogen bond is composed ofseveral constituent interactions which are variant in theircontributing weights. Chemical variation of donor and/oracceptor, and possibly also of the environment, can graduallychange a hydrogen bond to another interaction type. Thisshall be detailed here for the most important cases.The transition to pure van der Waals interaction is very

common. The polarity of XH or A (or both) in the arrayXH A can be reduced by suitable variation of X orA. This reduces the electrostatic part of the interaction,whereas the van der Waals component is much less affected.In consequence, the van der Waals component gains relativeweight, and the angular characteristics gradually change fromdirectional to isotropic. Since the polarities of XH or Acan be reduced to zero continuously, the resulting transition ofthe interaction from hydrogen bond to van der Waals type is

continuous too. Such a behavior was actually demonstratedfor the directionality of CH OC interactions, whichgradually disappears when the donor is varied from CCHto CCH2 to CCH3 (see Figure 8, Section 3.2).[22] At theacceptor side of a hydrogen bond, sulfur is typical of an atomthat allows continuous variation of the partial charge from S

to S. Therefore, one can create a continuum of chemicalsituations between the S atom acting as a fairly stronghydrogen bond acceptor, and being inert to hydrogen bonding(the extreme cases are ionic species such as XS andXSY).At the other end of the energy scale, there is a continuous

transition to covalent bonding.[28] In the so-called symmetrichydrogen bonds XHX, where an H atom is equally sharedbetween two chemically identical atoms X, no distinction canbe made between a donor and an acceptor, or a covalentXH and noncovalent H X bond (found experimentallyfor XF, O, and possibly N). In fact, this situation can beconveniently described as a hydrogen atom forming twocovalent bonds with bond orders s 12. In crystals (and also insolution), all intermediate cases exist between the extremesXH IX and XHX. Strongly covalent hydrogen bondswill be discussed in greater detail in Section 7, and the bondorders (valences) of H O over the whole distance rangewill be given in Section 9 (Table 7).There is also a gradual transition from hydrogen bonding to

purely ionic interactions. If in an interaction XH YH the net charges on XH and YH are zero, theelectrostatics are of the dipole dipole type. In general,however, the net charges are not zero. Alcoholic OH groupshave a partial negative charge in addition to their dipolemoment, ammonium groups have a positive net charge, and soon. This situation leads to ionic interactions between thecharge centers with the energy having a r1 distance depend-ence. If the charges are large, the ionic behavior may becomedominant. For fully charged hydrogen bond partners, ener-getics are typically dominated by the Coulombic interactionbetween the charge centers, but the total interaction stillremains directional, with XH not oriented at random butpointing at A. An important example are the so-called salt-bridges between primary ammonium and carboxylate groupsin biological structures,[5] NH O. If weakly polar XHgroups are attached to a charged atom, such as the methylgroups in the NMe4 ion, they are often involved in shortcontacts to an approaching counterion, NXH A.[8]Although these interactions are directional and may still beclassified as a kind of hydrogen bond, their dominant part iscertainly the ionic bond N A.Finally, there is a transition region between the hydrogen

bond and the cation interaction. In the pure cation interaction a spherical cation such as K contacts the negativecharge concentration of a -bonded moiety such as a phenylring. This can be considered an electrostatic monopole quadrupole interaction. The bond energy is 19.2 kcalmol1for the example of K benzene.[29] A pure -type hydrogenbond XH Ph is formally a dipole quadrupole inter-action with much lower energies of only a few kcalmol1

(Table 1). If charged hydrogen bond donors such as NH4

interact with -electron clouds, local dipoles are oriented at

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Table 1. Calculated hydrogen bond energies (kcalmol1) in some gas-phase dimers.[a]

Dimer Energy Ref.

[FHF] 39 [27a][H2OHOH2] 33 [27b][H3NHNH3] 24 [27b][HOHOH] 23 [27a]NH4 OH2 19 [27c]NH4 Bz 17 [27d]HOH Cl 13.5 [27c]OCOH OCOH 7.4 [27e]HOH OH2 4.7; 5.0 [27f,g]NCH OH2 3.8 [27h]HOH Bz 3.2 [27i]F3CH OH2 3.1 [27j]MeOH Bz 2.8 [27k]F2HCH OH2 2.1; 2.5 [27f,j]NH3 Bz 2.2 [27i]HCCH OH2 2.2 [27h]CH4 Bz 1.4 [27i]FH2CH OH2 1.3 [27f,j]HCCH CCH 1.2 [27l]HSH SH2 1.1 [27m]H2CCH2 OH2 1.0 [27l]CH4 OH2 0.3; 0.5; 0.6; 0.8 [27f,n p]CCH2 CC 0.5 [27l]CH4 FCH3 0.2 [27q][a] For computational details, see the original literature. Bz benzyl.

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the face,[30] but the energetics are dominated by the charge quadrupole interaction[27d] (NH4 Bz experimentally:19.3 kcalmol1).[29] If the XH groups of the cation areonly weakly polar, they may also orient at the face and causesome modulation of the dominant cation interaction, butthis modulation fades to zero with decreasing XH polarity.

2.6. Incipient Proton Transfer Reaction

A very important way of looking at hydrogen bondsis to regard them as incipient proton-transfer reactions.From this viewpoint, a stable hydrogen bond XH Y is afrozen stage of the reaction XH YX HY (orXH YX HY, etc.). This means that a partialbond H Y is already established and the XH bond isconcomitantly weakened.[31] In the case of strong hydrogenbonds, the stage of proton transfer can be quite advanced. Insome hydrogen bonds the proton position is not stable at X orY, but proton transfer actually takes place with high rates. Inother cases these rates are small or negligible.The interpretation of hydrogen bonds as an incipient

chemical reaction is complementary to electrostatic viewson hydrogen bonding. It brings into play acid base consid-erations, proton affinities, the partially covalent nature of theH Y bond, and turns out to be a very powerful concept forunderstanding the stronger types of hydrogen bonds inparticular. For example, the partial H Y bond can onlybecome strong if its orientation roughly coincides with theorientation of the full HY bond that would be formed uponproton transfer. Approach in different orientations may stillbe favorable in electrostatic terms, but results only inmoderately strong hydrogen bonds.This view also helps in deciding whether a particular type of

XH A interaction may be classified as a hydrogen bond ornot (compare the definition in Section 2.1). Only if it may bethought of as a frozen proton-transfer reaction, may it becalled a hydrogen bond.

2.7. Location of the H Atom

An atom is constituted of a nucleus and its electron shell.Normally, the centers of gravity of the nucleus and electronshell coincide well, and this common center is called thelocation of the atom. For H atoms, however, this isgenerally not the case. In a covalent bond with a moreelectronegative atom, the average position of the singleelectron of the H atom is displaced towards that other atom.The centers of gravity of the nucleus and electron no longercoincide, and this leads to a conceptual problem: what shouldbe taken as the location of the atom? It is not chemicallyreasonable to consider one of the two centers of gravity as theright location of the atom, and the other as wrong, butone must accept that a point-atom model is simplistic in thissituation.[32, 33] In practice, this leads to unpleasant complica-tions. X-ray diffraction experiments determine electron-density distributions and locate the electron-density maximaof the atoms. Neutron diffraction, on the other hand, locates

the nuclei. The results of the two techniques for H atoms oftendiffer by more than 0.1 .[34] Neither of the two results is moretrue than the other, but they are complementary and bothrepresent useful pieces of information. Nevertheless, neutrondiffraction results are much more precise and reliable, andallow the proton positions to be located as accurately as othernuclei.It has become a practice in the analysis of X-ray diffraction

results to normalize the XH bonds by shifting the positionfound for the H atom (that is, the position of the electroncenter of gravity) along the XH vector to the averageneutron-determined internuclear distance, namely, to theapproximate position of the proton.[35] This theoreticalposition is then used for the calculation of hydrogen bondparameters. The currently used standard bond lengths are:OH 0.983, NH 1.009, CH 1.083, BH 1.19, andSH 1.34 ; a more complete list can be found in ref. [8].The normalization procedure is generally reasonable, wellsuited to smooth out the large experimental uncertainty ofX-ray diffraction data, and is particularly useful in statisticaldatabase analysis. Nevertheless, one must be aware that it isnot a correction in the strict sense, instead it replaces a certainstructural feature (the location of the electron center ofgravity) by a chemically different one (the proton position).Furthermore, the internuclear XH bond length is fairlyconstant only in weak and moderate hydrogen bonds, whereasit is significantly elongated in strong ones. In the lattersituation, the elongation should at least in principle be takeninto account in the normalization. This requires, however,knowledge of the relationship between the relevant XH andH A distances (see Section 3.6).[36]

2.8. Charge Density Properties

The precise mapping of the distribution of charge density inhydrogen-bonded systems is a classical topic in structuralchemistry,[37] with a large number of individual studiesreported.[38] Currently, Baders quantum theory of atoms inmolecules (AIM) is the most frequently used formalism intheoretical analyses of charge density.[39] Each point in space ischaracterized by a charge density (r), and further quantitiessuch as the gradient of (r), the Laplacian function of (r),and the matrix of the second derivatives of (r) (Hessianmatrix). The relevant definitions and the topology of (r) in amolecule or molecular complex can be best understood withthe help of an illustration (Figure 2; see figure legend fordetails).[40] The thin lines represent lines of steepest ascentthrough (r) (trajectories). If there is a chemical bondbetween two atoms (such as a hydrogen bond), they aredirectly connected by a trajectory called the bond path. Thepoint with the minimal value along the bond path is calledthe bond critical point (BCP). It represents a saddle point of(r) (strictly speaking, trajectories terminate at the BCP, sothat the bond path represents a pair of trajectories each ofwhich connects a nucleus with the BCP). Different kinds ofchemical bonds have different numerical properties at theBCP, such as different electron density BCP and different

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Figure 2. Representative topology of a theoretical electron density func-tion in a hydrogen-bonded system: the adduct of chloroform and form-aldehyde formed through a CH O hydrogen bond.[40] Thin linesrepresent lines of steepest ascent through (r) (trajectories). Critical points(CP) of (r) are maxima and points where the first derivative vanishes.There are four types of CPs in three-dimensional space (rank 3, that is, non-degenerate). Maxima are denoted (3, 3) and minima (3, 3). The latterare also called cage critical points (CCP). Saddle points representing aminimum in one direction of space and maxima in two perpendiculardirections are called bond critical points (BCP) and denoted (3, 1).Saddle points, which represent minima in two perpendicular directions ofspace and a maximum in the third direction, are called ring critical points(RCP) and denoted (3, 1). The trajectories ending at a nucleus constitutea molecular basin. Basins of neighboring atoms are separated bytrajectories that do not end at nuclei (namely, the interatomic surface).Trajectories connecting nuclei through a BCP are called a bond path. Theelectron density at BCPs are minima in the bond paths and maxima in theinteratomic surface. BCPs are shown in the figure as squares.

values of the Laplacian function (negative for covalent bondsand H A interactions of very strong hydrogen bonds, andpositive for ionic bonds, van der Waals interactions, H Ainteractions of medium strength, and weak hydrogen bonds).The electron density at the bond critical point (BCP) is

higher in strong bonds than in weak ones. There are two bondcritical points in a hydrogen bond XH A, one between Xand H, and one between H and A. In normal hydrogen bonds,the BCP value in XH is much larger than in H A. Thevalue of BCP in H A increases with increasing hydro-gen bond strength, while that in XH decreases concom-itantly. In the ideally centered case, XHX, BCP is equal forboth bonds. This behavior has been nicely illustrated forOH O hydrogen bonds (Figure 3).[41] Bond paths with

Figure 3. Electron density at the bond critical points, BCP, for a set ofOH O hydrogen bonds, together with fitted logarithmic relationshipsfor experimental and theoretical data. (Adapted from ref. [41].)

significant values of BCP have been calculated also for weakerhydrogen bonds of the types CH O[40] and CH [27l] , aswell as for dihydrogen bonds.[42] Electron-density proper-ties of the agostic interaction relative to the hydrogen bondhave also been characterized.[43]

Hydrogen bond properties are sometimes discussed exclu-sively in terms of topological analysis of theoretical (r) dis-tributions. Despite the merits of the method, it is unfortunatethat discussion tends to be very formalistic, ocassionally evenoverriding conflicts with experimental data.

2.9. IR and NMR Spectroscopic Properties

IR and NMR spectroscopy have both become standardmethods to investigate hydrogen bonds in the solid state.[6]

Nevertheless, they are not the focus of the present article andare, therefore, only briefly touched on here.Formation of a hydrogen bond affects the vibrational

modes of the groups involved in several ways.[44] For relativelysimple systems, these effects can be studied quantitatively bysolid-state IR spectroscopy. If there are many symmetry-independent bonded groups, however, band overlap normallyprevents detailed analysis. The frequency of the donor XHstretching vibration (XH) is best studied because it is (forpolar XH groups) quite easy to identify in absorptionspectra, and in most cases very sensitive to the formation ofhydrogen bonds (red-shift of the absorption band, bandbroadening or intensification). For OH O hydrogenbonds, OH is correlated with the O O distance (Fig-ure 4).[45, 46] Analogous correlations have been established

Figure 4. Scatter plot of IR stretching frequencies OH against O Odistances in OH O hydrogen bonds (squares: combination of acid andcomplementary base; filled circles: resonance-assisted hydrogen bonds(RAHB); triangles: -cooperative hydrogen bonds; crosses: isolatedhydrogen bonds).[46] (IR data from ref. [45a].)

also for less common hydrogen bond types, for example,between the donor CCH and the acceptors O,[47] N,[48] andCC.[49] There is considerable scatter in these correlations, notjust because of experimental inaccuracy. The correlationsrepresent systematic trends between different physical quan-tities, but not strict laws (for the discussion of an example, seefootnote [50]).

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The difference between the XH value of free and hydro-gen-bonded XH groups,XH, increases systematically withdecreasing H A (or X A) distance. It has even beenreported that a common correlation XH f(H A) isapproximately valid for many different types of XH Ahydrogen bonds, and on the basis of a set of diverse organicand inorganic structures, it has been parametrized as XH0.011dHA6.1 (XH in cm1, d in nm).[51] An approximaterelationship with bond enthalpies has also been establishedfor OH O hydrogen bonds, H 0.134dHA3.05 (H inkJmol1, d in nm; the equivalent relationship with band shiftsis H 1.3 ()0.5).[51] The predictive power of these corre-lations is limited by the large scatter.Further important properties of XH are the band width

and the integrated band intensity I(XH). The band width andI(XH) increase strongly upon formation of a hydrogen bond,and this is often taken as a more reliable indicator of hydrogenbond formation than the red-shift of XH. For example, thereare cases of CH O hydrogen bonding where XH isdifficult to measure while the increase of I(XH) is easy todetect.[52] The increase of I(XH) has been correlated with thestrength of the hydrogen bond, and the approximate relation-ship H 12.2I(XH)0.5 was suggested.[53]In principle, the H A stretching vibration is the most

direct spectroscopic indicator of hydrogen bonding. Forweaker kinds of hydrogen bonds, these bands are in the farinfrared, and are investigated only rarely. A direct effect ofthe hydrogen bond can often be observed also on the acceptorside. In XH OC bonds, for example, the OC bond isweakened leading to a lowering of the stretching vibrationfrequency.The effects described above show many anomalies. For

example, bond energies and dissociation constants of CH O interactions of chloroform molecules are substantial, butCH may not only shift to lower, but also to slightly higherwavenumbers. The band intensity always increases, as usu-al.[54] This effect, long regarded only as an exotic anomaly, hasrecently attracted greater attention. According to theoreticalcalculations,[55] a blue-shift of CH indicates a different kind ofelectronic interaction in the hydrogen bond: electron densityof the acceptor is not mainly transferred into the antibonding* orbital of the donor XH, but into remote parts of thedonor molecule (such as the CCl part of CHCl3). Thistransfer of electron density is also associated with a shorteningof the XH bond. The term improper blue-shifting hydro-gen bonds was introduced to distinguish these interactionsfrom proper hydrogen bonds.In most hydrogen bonds several nuclei may be observed by

NMR spectroscopy. In particular, the proton is increasinglydeshielded with increasing hydrogen bond strength, whichleads to 1H downfield shifts that are correlated with the lengthof the hydrogen bond.[6, 56] Thus, NMR shift data can be usedto estimate lengths of hydrogen bonds (Figure 5). Chemicalshifts of X and A (for example, 15N), X/H and X/A couplingconstants, and differences in the 1H and 2H signals in H/Dexchange experiments can give additional information onXH A bonds. In OCOH N(Py) hydrogen bonds, forexample, the 15N chemical shift has been used to probethe protonation state of the N atom: in moderate strength

Figure 5. Typical correlation of 1H NMR chemical shift and O Odistance in OH O hydrogen bonds.[56c] Other authors have obtainedsimilar figures from different structure samples.[6, 56a,b]

OH N hydrogen bonds the shift is 20, in symmetricbonds OHN it is around 60, and in ionic bondsO HN it becomes 100.[57] The time scale of protondynamics in a disordered hydrogen bond can be determinedfrom NMR experiments in a certain frame (s scale)accessible to the experimental method.

2.10. The Categories of Strong, Moderate, andWeak Hydrogen Bonds

As we have seen, hydrogen bonds exist with a continuum ofstrengths. Nevertheless, it can be useful for practical reasonsto introduce a classification, such as weak, strong, andpossibly also in between. In this article, the systemdescribed by Jeffrey is followed,[6] who called hydrogen bondsmoderate if they resemble those between water molecules orin carbohydrates (one could also call them normal), and areassociated with energies in the range 4 15 kcalmol1. Hydro-gen bonds with energies above and below this range aretermed strong and weak, respectively. Some general proper-ties of these categories are listed in Table 2. It must be stressedthat there are no natural borderlines between these

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Table 2. Strong, moderate, and weak hydrogen bonds following the classifica-tion of Jeffrey.[6] The numerical data are guiding values only.

Strong Moderate Weak

interaction type stronglycovalent

mostlyelectrostatic

electrostat./dispers.

bond lengths []H A 1.2 1.5 1.5 2.2 2.2lengthening of XH [] 0.08 0.25 0.02 0.08 0.02XH versus H A XHHA XHH A XHH AX A [] 2.2 2.5 2.5 3.2 3.2

directionality strong moderate weak

bond angles [] 170 180 130 90

bond energy [kcalmol1] 15 40 4 15 4

relat. IR shift XH [cm1] 25% 10 25% 10%1H downfield shift 14 22 14

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categories, and that there is no point in using this or anyrelated system in too stringent a way. For a comment on thenames of the categories, see footnote [58].

3. Geometry

Hydrogen bonds and their environment have a well-definedgeometry in the crystalline state. More than 200000 publishedorganic and organometallic crystal structures provide a vastamount of experimental data that allows hydrogen bondgeometries to be analyzed at a high statistical level.[10] Theresults of such analyses are presented in this section.

3.1. Donor Directionality

The main structural feature distinguishing the hydrogenbond from the van der Waals interaction is preference forlinearity. As a typical example, the distribution of angles incarbohydrates is shown in Figure 6 (H O 2.0 ). Theabsolute frequencies peak between 160 and 170 (Figure 6a);these are the angles that occur most frequently in crystals. Toobtain the more relevant frequencies per solid angle, one mustweight the absolute values with 1/sin (cone correction).[59]

The weighted frequencies clearly peak at linear angles(Figure 6b).

Figure 6. Directionality of OHO hydrogen bonds in carbohydrates(H O 2.0 ). a) Conventional histogram with a maximum at slightlybent angles . b) Histogram after cone correction (weighting with 1/sin)which represents the frequency of H-bonds per solid angle.[59] Angularpreferences can be seen properly only after cone correction.

The histograms in Figure 6 do not contain distance infor-mation, and this is a significant disadvantage. A better (butmore costly) way to analyze angular preferences is in scatterplots of angles against distances d. This is illutrated for theexample of XH Cl interactions in Figure 7 (for hydroxydonors in Figure 7a and for NH3 donors in Figure 7b).[60] Theplots include all contacts found in crystal structures with d4.0 at any occurring angle. There are densly populatedclusters of data points at short distances and fairly linearangles, and each point in these clusters represents a hydrogenbond. The scatter within the clusters is considerable, and theirborders are diffuse. The shortest distances occur at relatively

Figure 7. Angular scatter plot of XH Cl angles against H Cldistances for a) hydroxy and b)NH3 donors (XH bonds normalized).[60]All contacts with H Cl 4.0 are included, whether they represent ahydrogen bond or not.

linear angles , whereas longer bonds are observed with alarger angular range. At longer distances and bent angles, aweakly populated region represents minor components ofbifurcated hydrogen bonds (Scheme 2). The regions to theright of these clusters are almost empty, which shows that verylong but linear hydrogen bonds almost do not occur (comparewith Figure 1). At long distances there is a region of randomscatter, which corresponds to XH groups and chloride ionsthat do not form a direct interaction. The plots are unpopu-lated at short distances, because exchange repulsion preventsshorter approach.The detailed appearance of the plots depends on the type of

donor. With the hydroxy group as a donor (Figure 7a), thepicture contains only the arrays mentioned above, and thehydrogen bond region is fairly well separated from the regionof random scatter. With the more complicated donorNH3(Figure 7b), there is an additional, densely populated featureat long distances and very bent angles 90. This newcluster represents the two H atoms ofNH3 that point awayfrom the chloride ion if a NH3 Cl hydrogen bond isformed. There is a much higher density of bifurcated hydro-gen bonds in Figure 7b than in Figure 7a, and all thepopulated regions merge into each other. Plots analogous toFigure 7 have been published for other special kinds of

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hydrogen bonds, such as OH O[61] and CH O inter-actions in carbohydrates,[62] and with more-limited angularranges for general OH O and NH O,[63] water wa-ter,[64] N/OH Ph,[65] CH Cl(C),[66] and even CH F(C)[67] hydrogen bonds. These figures all show the samegeneral features (preference of linearity) with some variationin the details, which indicates that the angular characteristicsof all kinds of hydrogen bonds are related.The degree of directionality depends on the polarity of the

donor. This effect is shown in Figure 8 with cone-correctedangular histograms of normal hydrogen bonds OH OC,of CH OC interactions with three CH types of differentpolarities, and, for comparison, also of CH HC van derWaals contacts.[22] The degree of directionality decreases inparallel with the polarity of the XH group, namely, OHCCHCCH2CH3. Note that CH O contacts ofmethyl groups still show a weak but significant preference forlinearity that is clearly different from van der Waals contacts.This is experimental evidence that methyl CH O inter-actions deserve to be classified as hydrogen bonds (very weakones, though).

Figure 8. Directionality of XH OC interactions with XH groups ofdifferent polarities (cone-corrected angular histograms). a) Hydroxy,b) CCH, c) CCH2, d)CH3 donors, e) CHHC van der Waalscontacts. The degree of directionality decreases gradually from (a) to (d),and interaction (e) is isotropic within a broad angular range. Note that thepicture for CCH is similar to that for the conventional OH donor.CHOC interactions of methyl groups are still directional, but to amuch smaller extent than CCH OC hydrogen bonds.[22]

3.2. Acceptor Directionality

Hydrogen bonds are directional also at the acceptor side.For strong hydrogen bonds (but only for these essentially), thedirectionality of the acceptor corresponds to the geometry ofthe covalent product obtained in a hypothetical proton-

transfer reaction. The directionality of moderate and weakhydrogen bonds is much softer, but can still be identified withthe orientation of electron lone pairs (in rare cases[68] also withfilled dz2 orbitals of transition metal atoms). In the classicalexample of carbonyl groups, the oxygen lone pair lobes are inthe R2CO plane and form angles of about 120 with the CObond. As is seen in an angular histogram with N/OH donors(Figure 9, bottom), a corresponding acceptor directionality isindeed present, but it is softer than is often assumed.[69] Asimilar distribution has also been found with stronger types ofCH donors (CCH, Cl3CH, Cl2CH2).[70] It is interesting thatthe acceptor directionality is much more pronounced forthiocarbonyl groups, with lone pair directions forming anangle of only 105 with CS (Figure 9, top).[69] The CSe Hangle in selenocarbonyl acceptors is even closer to rectangu-lar.[8]

For hydroxy and water acceptors, the electronic structurewould predict a bimodal distribution with two preferreddirections in roughly tetrahedral geometry with respect to the

Figure 9. Acceptor directionality of CO (bottom) and CS (top) groupsin N/OH O/SC hydrogen bonds.[69] Note that the directionality ismuch more blurred for CO than for CS.

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two covalent bonds at the O atom. The actual directionality,however, is so soft that clustering is only observed in thebisecting plane of R1OR2, without separation into twomodes.[71] The acceptor directionality of the pyridyl N atomhas also been characterized in a statistical study.[72]

Of more recent interest are hydrogen bonds with halogenacceptors. A metal-bonded halogen atom is strongly polar anda good acceptor. The electronic structure suggests differentbasicity characteristics of the different electron lone pairs(Scheme 3),[73] and indeed, XH ClM hydrogen bonds incrystals are almost exclusively donated roughly perpendicularto the MCl bond (angular range 80 140).[73, 74] An excep-tion among the metal-bonded halogens is fluorine, whichshows a much more isotropic behavior.[75]

M Halsp-type lone pair(less basic)

p-type lone pair(more basic)

Scheme 3. The electron lone pairs of metal-bonded halogen.[73]

Most complex, and not yet fully explored, is the direction-ality of acceptors. For the simplest one, CC, it seems thathydrogen bonds are preferably directed at the midpoint of thetriple bond, but may point also at individual C atoms.[8] Forthe most important acceptor, the Ph group, the potentialenergy surface of XH Ph interactions is very flat, whichallows large movements of the donor over the face withoutmuch of a difference in energy.[27i,k, 76] Consensus has not beenreached concerning the location of the global energy mini-mum: does it occur with the XH vector exactly over the ringmidpoint (then, XH can interact with all electrons of the system), or does XH point at an individual CC bond oreven a C atom? All these geometries, and also all intermedi-ate situations, are found in crystals. Two extreme cases areillustrated in Figure 10 (for details, see legend).[77, 78] The largesize of the face makes the Ph acceptor a target that is easyto hit.[79] This has important consequences for the role of thephenyl group in the packing of organic molecules,[8] and alsofor its role as a reserve acceptor in biological substances.[80] Inthe case of a local deficiency of conventional acceptors, adonor can form an XH Ph hydrogen bond instead if a Phgroup is available even only in a roughly suitable geometry.

3.3. Distributions and Mean Values of the H A BondLengths

Hydrogen bond lengths d in the solid state are very variable.Distances and angles vary in wide ranges even with a constantdonor acceptor combination, as shown already for theexample COH Cl in the d scatter plot shown inFigure 7a. Here, the broad scatter can not be a consequenceof chemical variations, but only of crystal packing forces thataffect each hydrogen bond in a different way (for a moredetailed discussion of this matter, see Section 5).

Figure 10. OH Ph hydrogen bonds with different geometries. a) Thedonor is positioned almost exactly over the aromatic midoint M ; the sixH C distances are in the range 2.49 2.70 ; H M is much shorter,2.17 , and the OH M angle is 160 (X-ray crystal structure of cholinetetraphenylborate).[77] b) The donor is oriented directly at a C atom, H C 2.34 , angle OH C 174 (neutron diffraction crystal structureof 5-ethynyl-5H-dibenzo[a,d]cyclohepten-5-ol).[78]

If one wants to display bond lengths in a histogram, a cutoffin the angle has to be selected. If only linear hydrogenbonds are of interest, one may select 135 and arrive ata distribution such as the one shown in Figure 11a forNH3 Cl hydrogen bonds. There is a distinct maximum,and the distribution has a well-defined beginning and a fairly

Figure 11. Typical H A bond-length distributions: NH3 Cl hydro-gen bonds up to a cutoff of d 3.0 (data as for in Figure 7b). a) Onlyfairly linear hydrogen bonds with 135. This histogram contains datafrom a horizontal slice 180 135 of Figure 7b. b) With the generousangle cutoff 90. This histogram contains data from the slice 18090 of Figure 7b.

well defined end with only a few outliers. For weak hydrogenbond types (or severely sterically hindered ones), thedistribution does not fall to zero at long distances but fadesinto the continuum of random contacts.[81] If a more generous

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angle cutoff is chosen, such as 110 or 90, the distancedistribution will typically look like the one in Figure 11b.Minor components of multifurcated interactions are nowincluded, and as a consequence, the distribution no longergoes to zero at longer distances: following a certain minimum,the frequency of contacts increases again and merges with thecontinuum of random contacts. Since the relative content ofmultifurcated bonds is strongly sample-dependent (see Sec-tion 3.4), the exact shape of the long-distance region of suchhistograms is strongly sample-dependent too. Statistical

characterization of such distributions (such as Figure 11b) isdifficult.[82]

Figures 7 and 11 show the geometry variation for a constantdonor acceptor combination. If the donor and/or acceptorare chemically varied, new pictures are obtained which differin the mean distance and the degree of directionality.Relatively comprehensive (and new) numerical data arecompiled in Tables 3 and 4 for hydrogen bonds involvingwater molecules to shed light on the general rules determiningmean hydrogen bond lengths.[10]

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Table 3. Hydrogen bonds with water molecules as acceptors (XH OW): Geometry of fairly linear interactions ( 135) with various donors (distancesare given in ). (Database information was retrieved for this article.[10a])

Donor n Mean H OW distance Mean X OW distance H OW distance (95%)[a] X OW distance (95%)[a]

OH donorsH3O 21 1.54(2) 2.49(2) NOH 1 1.57( ) 2.55( ) SOH 4 1.58( ) 2.55( ) POH 73 1.61(1) 2.575(9) 1.44 1.77 2.42 2.72SeOH 4 1.62( ) 2.59( ) OCOH 244 1.629(4) 2.591(4) 1.51 1.78 2.49 2.75NCOH 6 1.69(3) 2.60(3) NOH 46 1.68(1) 2.65(1) CCOH, PhOH 162 1.724(8) 2.679(7) 1.55 1.96 2.52 2.88AsOH 4 1.75( ) 2.68( ) OOH 2 1.76( ) 2.69( ) Csp3OH 763 1.804(4) 2.753(3) 1.64 2.06 2.61 2.973(TM)OH[b] 6 1.81(5) 2.76(4) 2(TM)OH[b] 14 1.85(4) 2.79(4) H2O 2505 1.880(2) 2.825(2) 1.72 2.19 2.68 3.11BOH 5 1.91( ) 2.86( ) TMOH[b] 5 1.96( ) 2.89( ) OH 2 2.27( ) 3.22( )

NH donors(SO2,SO2)NH 7 1.71(1) 2.70(1) ImNH 20 1.74(2) 2.73(2) PyNH 67 1.78(1) 2.75(1) 1.63 2.05 2.63 2.96(C,C,C)NH 40 1.82(2) 2.77(1) (C,C)NH2 108 1.87(1) 2.83(1) 1.68 2.19 2.68 3.06(Csp2,Csp2)NH 316 1.860(8) 2.835(7) 1.69 2.20 2.69 3.13CNH3 370 1.878(6) 2.840(5) 1.71 2.17 2.71 3.08NH4 86 1.95(1) 2.91(1) 1.74 2.24 2.73 3.11(Csp2,Csp3)NH 178 1.988(9) 2.937(8) 1.79 2.25 2.77 3.18(peptide)NH 118 1.99(1) 2.94(1) 1.80 2.31 2.77 3.18Csp2NH2 508 2.016(6) 2.963(5) 1.81 2.31 2.78 3.21(TM,C,C)NH[b] 128 2.05(1) 2.99(1) 1.82 2.35 2.82 3.24(TM,Csp2)NH[b] 18 2.07(3) 3.03(3) (TM,C)NH2[b] 467 2.084(6) 3.031(5) 1.88 2.35 2.86 3.27TMNH3[b] 68 2.09(2) 3.03(1) 1.90 2.35 2.89 3.28(Csp3,Csp3)NH 13 2.14(3) 3.08(2) Csp3NH2 20 2.12(4) 3.09(4) NNH2 5 2.16( ) 3.09( ) SH donorsCSH 1 2.16( ) 3.48( ) CH donorsCl3CH 2 2.06( ) 3.07( ) CCH 3 2.10( ) 3.16( ) Cl2CH2 2 2.16( ) 3.22( ) (N,N)Csp2H 32 2.41(3) 3.38(3) (Cl,C)Csp3H 6 2.46(9) 3.44(5) (N,C)Csp2H 276 2.48(1) 3.47(1) 2.12 3.14(C,C)Csp2H 1369 2.553(4) 3.540(4) 2.22 3.23(C,C,C)Csp3H 29 2.59(2) 3.59(2) OCH3 80 2.59(2) 3.59(2) 2.32 3.32Csp3CH3 533 2.632(6) 3.613(6) 2.37 3.35[a] The 95% ranges of H OW and X OW distances include 95% of the hydrogen bonds. They are given only if n 50. For distributions without apronounced maximum, the 2.5th percentile is given instead of the central 95%. [b] TM transition metal atom.

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Table 4. OWH A hydrogen bonds from water donor molecules that are not coordinated to transition metal atoms. Geometry of fairly linear interactions( 135) for various acceptors (distances in ). (Database information was retrieved for this article.[10b])

Acceptor n Mean H A distance Mean OWA distance H A distance (95%)[a] OW A distance (95%)[a]

O acceptorsOH 8 1.71(3) 2.69(3) SeO 6 1.79(2) 2.74(2) AsO 11 1.84(3) 2.76(2) PO, PO 664 1.846(4) 2.793(4) 1.69 2.09 2.65 3.01NO 50 1.84(2) 2.80(1) 1.66 2.12 2.64 3.03(C,C)CO 95 1.85(1) 2.80(1) 1.62 2.17 2.59 3.11COO 1035 1.859(4) 2.807(3) 1.72 2.07 2.69 2.99H2O 2505 1.880(2) 2.825(2) 1.72 2.19 2.68 3.11R2CO 2485 1.900(3) 2.840(2) 1.73 2.23 2.69 3.11Csp3OH 757 1.891(4) 2.831(4) 1.73 2.19 2.69 3.07TMOC[b] 560 1.902(6) 2.842(6) 1.66 2.24 2.63 3.12SO, SO 668 1.914(5) 2.854(4) 1.74 2.27 2.70 3.15BOC 23 1.92(3) 2.86(2) TMO, TMO[b] 218 1.94(1) 2.877(8) 1.73 2.30 2.70 3.16TMO2[b] 16 1.95(3) 2.88(2) PhOH 89 1.97(1) 2.89(1) 1.72 2.27 2.62 3.17COC 254 1.978(9) 2.910(7) 1.78 2.33 2.74 3.17NOH 20 1.99(3) 2.91(2) POH 34 1.97(2) 2.91(2) NO3 195 2.00(1) 2.927(9) 1.77 2.36 2.69 3.24(OC)OH 35 2.01(3) 2.94(3) SbOC 20 2.03(4) 2.95(3) ClO4 180 2.07(1) 2.98(1) 1.80 2.36 2.73 3.25TeOH 5 2.07( ) 2.99( ) CNO2 57 2.13(2) 3.04(2) 1.85 2.38 2.80 3.17TMCO[b] 4 2.30( ) 3.11( ) N acceptorsCsp3NH2 17 1.88(2) 2.84(1) Csp3, Csp3NH 23 1.93(3) 2.89(2) NNN 13 1.94(2) 2.89(2) Csp3, Csp3, Csp3N 78 1.96(1) 2.90(1) 1.78 2.27 2.76 3.20CNC 345 1.959(6) 2.905(6) 1.79 2.26 2.75 3.17CNO 24 1.99(3) 2.94(2) CN 43 2.00(2) 2.94(2) Csp2NH2 25 2.03(3) 2.95(2) CNN 50 2.03(2) 2.96(2) CNS 9 2.09(6) 3.03(5) S acceptorsCS 68 2.38(1) 3.31(1) 2.22 2.61 3.19 3.51PS, PS 12 2.35(2) 3.31(1) SnS 7 2.41(2) 3.33(3) R2CS 73 2.42(1) 3.36(1) 2.26 2.65 3.24 3.58TMSC[b] 16 2.51(3) 3.43(3) CSC 2 2.60( ) 3.53( ) Se acceptorsSe 3 2.45( ) 3.40( )

Halogen acceptorsF 13 1.70(2) 2.67(2) SiF62 12 1.84(2) 2.79(2) TMF[b] 45 1.85(3) 2.80(2) BF4 34 2.01(3) 2.94(3) PF6 18 2.08(3) 2.98(3) CF 5 2.19( ) 3.07( ) Cl 1013 2.245(3) 3.196(3) 2.10 2.46 3.06 3.38TMCl[b] 232 2.349(9) 3.272(8) 2.15 2.62 3.11 3.51CCl 30 2.77(5) 3.62(5) Br 233 2.415(8) 3.350(7) 2.25 2.66 3.21 3.61TMBr[b] 17 2.56(4) 3.47(4) CBr 1 2.83( ) 3.66( ) I 47 2.68(1) 3.61(1) TMI 6 2.90(8) 3.74(6) acceptorsPh 25 2.50(4) 3.38(4) CC 2 2.51( ) 3.35( ) CC 20 2.73(4) 3.57(4) Py 4 2.79( ) 3.72( )

[a] The 95% ranges of the H A and OWA distances include 95% of the hydrogen bonds. They are given only if n 50. For distributions without apronounced maximum, the 2.5th percentile is given instead of the central 95%. [b] TM transition metal atom.

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Mean distances are listed in Table 3 for fairly linear XH OW hydrogen bonds (Wwater molecule) from 47 XHdonor types (XO, N, S, and C). If one uses the ranking ofdistances to define a donor strength of XH, one finds ageneral ranking OHNH SHCH. These are onlyrough categories, however, with strong internal variations.Hydrogen bonds of the strongest CH types (Cl3CH, CCH)are clearly shorter on average than those with the weakestNH donors (Csp2NH2, NNH2). The ranking within theXH groups follows a simple rule: basically, the donorstrength is increased by neighboring electron-withdrawinggroups and reduced by electron-donating groups. In conse-quence, the ranking of OH donor strengths is H3OOCOHPhOHCsp3OHH2OOH. The differ-ence in mean bond lengths D within this sequence amountsto over 0.7 ! Remember, however, that each of the lines inTable 3 corresponds to a broad histrogram (such as inFigure 11a). The corresponding 95% ranges are normallyover 0.3 broad (last two columns in Table 3), which impliesthere are large overlapping regions of hydrogen bond geome-tries between most donor types.An analogous list is given in Table 4 for water OWH A

hydrogen bonds with 61 different acceptor types (AO, N, S,Se, halogen, system). It is clear that acceptor strengths areincreased by neighboring electron-donating groups andreduced by electron-withdrawing groups. The ranking ofstrengths for O acceptors is OHCOOH2OCsp3OHPhOHCNO2MCO, with mean bondlengths varying by 0.6 . A broad range of acceptor strengthsis also observed for fluorine: FMFBF4CF.Tables 3 and 4 summarize the data for H2O as an acceptor

and a donor, respectively. A more comprehensive picturewould require data for all donor acceptor combinations. TheXH and A groups from Tables 3 and 4 would fill a 48 61matrix with almost 3000 entries, too many to be discussed inpractice. Sections of this matrix have been published for thespecial cases of XH Hal,[60] CH O and CH N,[83]and CH [84] hydrogen bonds.General properties of donor acceptor matrices are best

discussed with smaller example matrices, such as those inTables 5 and 6. Part of the OH O matrix with four donors,and four acceptors that cannot act as donors simultaneously(CO, etc.) is shown in Table 5. The ranking of the donorstrength is here independent of the acceptor, and the rankingof the acceptor strength is independent of the donor.A related matrix is shown in Table 6 for four kinds of OH

groups acting as donor as well as acceptor. Here, theimportant observation is that strong donors are weak accept-ors, and vice versa. The OH group of the carboxylic acid, for

example, is a very strong donor but a very poor acceptor. Thewater molecule is a good acceptor but only a moderate donor.The distance properties d and D discussed above might

indicate that donor and acceptor strengths are integralproperties of any group XH or A. The shortest hydrogenbonds could then be made by simply combining the strongestdonor with the strongest acceptor. Such a view is correct in theelectrostatic regime of hydrogen bonds, namely, for thosedefined as moderate and weak in Section 2.10. It is notcorrect, however, for strong hydrogen bonds, where the lawsof covalent bonding and of proton transfer phenomenabecome dominant (see Section 7). For example, if one triesto make a short OH O bond by simply combining thestrongest donor from Table 3 (H3O) with the strongestacceptor in Table 4 (OH) a proton transfer will occur(H2OH OHH2O HOH) which leads to a moder-ate hydrogen bond between water molecules. Similarly, itwould be wrong to assume a strict relationship betweenhydrogen bond length and energy. Hydrogen bonds involvingions generally have a higher dissociation energy than thosebetween neutral molecules (this is a trivial consequence of theCoulombic attraction of the net charges), but need not havemuch shorter bond lengths (see, for example, the chargedacceptor NO3 in Table 4, with a long average O OWdistance of 2.97 ).

3.4. Bifurcated Hydrogen Bonds

In a multifurcated hydrogen bond, a donor forms hydrogenbonds with more than one acceptor simultaneously(Scheme 2). Multifurcated hydrogen bonding requires a highdensity of acceptors, at least locally (Scheme 2). Over 25% ofall OH O hydrogen bonds in carbohydrates are multi-furcated, and this fraction is even higher in amino acids.[6]

Proteins also contain multifurcated hydrogen bonds in largenumbers.[85] It is not always easy to show that all componentsare bonding, in particular if angles are small and/or some ofthe putative acceptors are forced by stereochemistry to beclose to the donor. For a number of bifurcated bonds,however, bond paths in the theoretical electron density havebeen shown for both components.[86]

As a consequence of their geometry, certain chemicalgroups are involved in these interactions with a particularlyhigh frequency. A typical example of the ortho-dimethoxy-phenyl group is shown in Scheme 4. In a database analysis,[10c]

31 OH O hydrogen bonds with this group were found, andof these, only 10 involve just one acceptor, whereas 21

62 Angew. Chem. Int. Ed. 2002, 41, 48 76

Table 5. Intermolecular OH O hydrogen bonds with acceptors that cannotact as donors (mean O O distances in , sample size in square brackets).(Database information was retrieved for this article.[10a])

Donor AcceptorCOO R2CO COC CNO2

OCOH 2.544(3) [421] 2.644(1) [1491] 2.72(2) [29] 2.80( ) [3]PhOH 2.65(1) [57] 2.734(5) [412] 2.812(2) [58] 2.96(3) [11]Csp3OH 2.736(5) [354] 2.824(2) [2567] 2.885(4) [764] 3.00(1) [74]HOH 2.807(3) [1035] 2.840(2) [2485] 2.910(7) [254] 3.04(2) [57]

Table 6. Intermolecular OH O hydrogen bonds: Donor acceptor matrixwith OH groups that can act as donors as well as acceptors (mean O Odistances in , sample size in square brackets). (For this article databaseinformation was retrieved.[10a])

Donor AcceptorHOH Csp3OH PhOH (OC)OH

HOH 2.825(2) [2505] 2.831(4) [757] 2.89(1) [89] 2.94(3) [35]Csp3OH 2.753(3) [763] 2.792(2) [4249] 2.84(1) [94] 2.89( ) [3]PhOH 2.679(7) [144] 2.721(7) [145] 2.807(6) [305] 2.97( ) [2]OCOH 2.591(4) [244] 2.646(6) [162] 2.69(2) [8]

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(68%) are bifurcated. Of thelatter, 8 are almost symmetric, withthe two H O distances differingby less than 0.2 .A strongest (major) component

can be clearly identified in mostmultifurcated hydrogen bonds, butnot always. Even trifurcated hydro-gen bonds occur occasionally with afairly symmetric geometry. The tri-ethanolammonium cation, for ex-ample, is always found in crystalstructures in very similar bowl-shap-ed conformations with the threehydroxy O atoms converging to-ward the NH donor (Fig-ure 12).[77, 87]

Frequently, the two acceptors of a bifurcated hydrogenbond are of different types, A1 and A2. If one is much weakerthan the other (such as with A1O, N, and A2HalC, ,etc.) it may be difficult to assess if it is actually of anystructural importance. However, numerous examples ofbifurcated hydrogen bonds have been found with a strongand a weak acceptor, occasionally even with the interactiongeometry more favorable to the weaker acceptor(Scheme 5).[88]

Figure 12. Trifurcated hydrogen bond in the triethanolammonium cationas seen in the neutron diffraction crystal structure of the dihydratedtetraphenylborate salt.[87] The three NH O hydrogen bonds have verysimilar geometries (H O 2.14 2.35, N O 2.71 2.86 , NH O 108 112).

O HO

X H

OH

OO H

O

F

a) b) c)

Scheme 5. Examples of bifurcated hydrogen bonds with a strong and aweak acceptor: a) with O and CC acceptors;[8, 88a,b] b) with O and Phacceptors;[80, 88c] c) with O and FC acceptors.[88d]

3.5. H H Contacts

The matter of short repulsive H H contacts is oftenoverlooked when interpreting hydrogen bond geometries. If ahydrogen bond is formed between two XH groups (or anXH and an YH group), the two may be roughly in-line sothat the H atoms are far apart from each other, but they mayalso form an angle in such a way that the H atoms approachquite closely (Figure 13). In database analyses of inorganic[89]

and organic[90] crystal structures, a lower limit of 2.05 was

Figure 13. Typical examples of short H H contacts in OH OHhydrogen bonds found by neutron diffraction studies of carbohydrates.[90]

found for H H contacts in such configurations. This does notaffect linear hydrogen bonded chains very much, but itimposes serious constraints on the geometry of circular arraysof hydrogen bonds. Short H Hcontacts cannot be avoided inrings of three hydroxy groups orwater molecules in particular(Scheme 6). They force angles to be very bent, and probably arethe reason why these rings arevery rare. Fairly short H Hcontacts occur also in cyclichydrogen-bonded dimers anddestabilize such arrays, for ex-ample, in the carboxylic aciddimer with H H contacts ofabout 2.34 (Scheme 7) andmany related patterns.

3.6. Influence on CovalentGeometry

Hydrogen bonding affects thecovalent geometry of the mole-cules involved. The lengtheningof the covalent XH bond was already described in the1950s,[91] and the correlation of the OH and H O distancesin OH O interactions has been studied many times withincreasing precision. The current correlation based on low-temperature neutron diffraction data is shown in Fig-ure 14a.[92] The OH bond continuously elongates withdecreasing H O distance until a symmetric geometryOHO is reached at an O O separation of about 2.39 .

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OO MeMe

OH

Scheme 4. Example ofa functional groupwith a strong tendencyto accept bifurcatedhydrogen bonds (21out of 31 hydrogenbonds found in a CSDanalysis were bifurcat-ed).[10c]

O O

OH

H

H

2.07

2.21

Scheme 6. Short H H con-tacts are unavoidable in ringsof three OH O hydrogenbonds. The mean geometryin crystals is: d 2.07(3) ,D 2.89(2) , 143(2),H H 2.21(3) .[10d]

O H

O

O

H O2.34

1.225

1.316

113.6o

123.1o1.64

Scheme 7. Mean geometry ofthe carboxylic acid dimer incrystals.[10e] Note the shortdestabilizing H H contact.The mean O O distance is2.644 .

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Figure 14. Lengthening of the XH bond in XH A hydrogen bonds.a) Correlation of OH and H O distances in OH O hydrogenbonds.[92] The plot is symmetrized with respect to the two O atoms.[31b]

b) Correlation of NH with H O bond lengths and OH with H Nbond lengths.[93] The right branch shows NH O, and the left branchOH N hydrogen bonds. Both plots are based on neutron diffractiondata.

The correlation is perfectly smooth. There is no indication of acritical distance at which the hydrogen bond switches fromone interaction type to another. The elongation is in the range0.02 0.08 for moderate hydrogen bonds (Table 2), but it isup to 0.25 for strong ones. The analogous scatter plot forNH O and OH N hydrogen bonds also shows a smoothcorrelation (Figure 14b),[93] with the geometrically symmetricbond occuring at an N O distance of about 2.50 . Analternative way to illustrate the elongation of XH bonds is todraw XH and H A distances as a function of the X Aseparation, as shown in Figure 15 for the example ofO/NH N/O bonds.Lengthening of the XH bond has been found for

many other kinds of XH A hydrogen bonds, andseems typical of hydrogen bonding. The effect has beendescribed for NH N,[94] OH S,[36] NH S,[36]OH Cl,[36] NH Cl,[36] and CH O[95] interactions,although the full range of geometries has been explored onlyfor the types shown in Figure 14. For some special systems,

Figure 15. Correlation of OH and H O bond lengths with the O Ndistance in O/NH N/O hydrogen bonds (neutron diffraction data).[93]

quantum chamical calculations predict shortening, not length-ening, of the XH bond,[55, 96] but there is no consensus on thisamong theorists[27l] and experimental structural proof is stilllacking.XH A hydrogen bonding also affects the angles at X

(Scheme 8). For the example ofNH3 Cl hydrogen bonds,the bending of the CNH angle as a function of the

O H O O HO

O H

OScheme 8. Bending of the XOH angle in OH A hydrogen bonds.

CN Cl coordination angle is shown in Figure 16.[36] Thechange in the angle between the covalent bonds follows thatin the coordination angle, but is much smaller. Related plotshave been given for the bending of COH groups, and forthe opening and narrowing of the water angle by OH Oand OH Cl hydrogen bonds.[97] The bending typicallyamounts to only a few degrees, which is easy to see withneutron diffraction, but difficult to discern in X-ray diffractionstudies.

Figure 16. Bending of the CNH angle in NH Cl hydrogen bonds(NH3 donors, neutron diffraction data).[36]

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Torsional angles in molecular fragments may be influencedby hydrogen bonds to a degree that depends on the height ofthe torsional barrier between energy minima. The OH bondin a hydroxy group Csp3OH, for example, prefers to bestaggered with repect to the substituents at C (Scheme 9a). In

X O H X OH

Oa) b)

Scheme 9. Effect of hydrogen bonding on torsional angles. a) Free, andb) hydrogen-bonding hydroxy group.

crystal structures, on the other hand, the torsion angle aroundCO takes any value. If this angle is plotted against theXCO O dihedral coordination angle, it is seen that theOH vector is always rotated towards the acceptor, even intoan eclipsed orientation (Scheme 9b and Figure 17).[98] The

Figure 17. Rotation of hydroxy groups away from a staggered conforma-tion as a result of hydrogen bonding: the XCOH torsion angle adjuststo the XCC O dihedral coordination angle.[98]

same kind of analysis can be performed for methyl groups ofthe type Csp3CH3 involved in CH O interactions. In thiscase, the torsional barrier is far too high (typically 3 5 kcalmol1) to reach the eclipsed conformation. Neverthe-less, rotations of up to 10 15 from the ideally staggeredconformations have been detected, which corresponds to adisplacement of the H atoms by 0.2 from their idealizedpositions.[98] A single case of an eclipsed methyl groupassociated with three CH O bonds has been reported,[99]but theoretical calculations show that the torsional barrier inthis particular molecule is dramatically reduced to about1.5 kcalmol1.[100]

The effects discussed above concern distances and anglesdirectly involving the H atom. There are also changes in thecovalent geometry of the non-hydrogen molecular skeleton of

both participating molecules. These effects are modest formoderate, and negligible for weak hydrogen bonds, but theycan become very large for strong ones. In a COH OChydrogen bond, for example, the CO bond is shortened andthe OC bond is lengthened compared to the free mole-cules.[101] In the extreme case of the symmetric hydrogen bond,the two CO bond lengths become identical, CO H OC. Figure 18 shows that the difference of the two COdistances depends linearly on the O O distance (note thatthe effect is already quite large with O O 2.6 ).[46]Carboxylate groups that accept one hydrogen bond becomeunsymmetric, and the CO bond involving the acceptingO atom becomes several hundreths of an longer than theother one (see, for example, ref. [102]).

Figure 18. Effect of COH OC hydrogen bonding on CO bondlengths. The quantity d is the difference between the donor CO and theacceptor OC bond length (d0 value for fragments free of hydrogenbonding; squares: combination of acid and complementary base; dots:resonance-assisted hydrogen bonds).[46]

All these correlations can be easily rationalized if they areinterpreted as mapping a proton-transfer reaction. Thegeometry of the donor molecule changes in the direction ofthe deprotonated species, and the geometry of the acceptingmolecule changes in the direction of a protonated one. Thishas been nicely demonstrated by suitable chemical variationsof substituted phenol amine adducts[103] to formmolecular orionic adducts, and also into intermediate cases.[104] A plot ofthe phenolic CO bond length against the O N distancegives the correlation shown in Figure 19. The data in the upperright corner show normal phenolic CO bond lengths ofaround 1.34 , and are associated with moderate strengthOH N hydrogen bonds. As the hydrogen bonds becomeshorter, the H atom is gradually abstracted and the CO bondshortens. The data in the bottom right corner show aphenolate CO bond length of 1.25 , and are associatedwith ionic hydrogen bonds NH OC. The symmetricsituation CO H N is reached at an N O distance ofabout 2.50 .A related effect is observed for the CNC angle in

pyridine molecules (Figure 20).[10f] The neutral pyridinemolecule has an angle at the nitrogen atoms of 116.6,[105]

whereas in pyridinium ions they are widened to 121 123 (forexample, 122.6 in Py HCl HCl[106]). This angle in OH N

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Figure 19. Effect of hydrogen bonding on the phenolic CO bond length.Data from adducts of phenols and amines.[103]

Figure 20. Effect of hydrogen bonding on the CNC angle in pyridine.[10f]

hydrogen bonds is increasingly widened as the hydrogen bondbecomes shorter (lower branch of the curve), and it isnarrowed in NH O hydrogen bonds as the bond becomesshorter. The branches meet again at O N 2.50 , with anangle at N of 120. Changes in covalent geometry also play animportant role in the case of resonance-assisted hydrogenbonding (see Section 4.2).

3.7. H/D Isotope Effects

The H/D isotope effect is a curious matter in the area ofhydrogen bonds. In the classical Ubbelohde effect, hydrogenbond lengths slightly increase upon deuteration.[107] This isthought to be a result of the lower zero-point vibrationalenergy of the OD relative to the OH bond, which makesthe OD bond more stable. In consequence, D is moredifficult to abstract from O than H, and the hydrogen bondsare weaker. The Ubbelohde effect has been examinedexperimentally for only a few OH/D O pairs. From arecent survey it appears that the isotope effect is strongest inthe O O distance range 2.5 2.6 (Figure 21).[108] It is muchsmaller for long hydrogen bonds, and about zero for very shortones (possibly, even negative values are allowed). The detailsof the effect are as yet unexplained.Isotope exchange occasionally leads to more severe struc-

tural changes. A well-studied example is trifluoroacetic acid

Figure 21. H/D isotope effect on hydrogen bond lengths. The differenceof O O distances in pairs of D and H compounds is plotted against theO O distance of the H compound. A value of 0 means that thehydrogen bond in the D compound is longer.[108]

tetrahydrate, which is cationic in the protonated form,F3CCOO 3H2O H3O, whereas it becomes molecularwhen deuterated, F3CCOOD 4D2O.[109]

4. Non-Additivity

Many properties of n interconnected hydrogen bonds arenot just the sum of those of n isolated bonds. Two principalmechanisms are responsible for this non-additivity, and bothoperate by mutual polarization of the involved groups.

4.1. -Bond Cooperativity

If an XH group forms a hydrogen bond XH A, it becomes more polar. The same is true if it accepts ahydrogen bond, YH XH. Thus, in a chain withtwo hydrogen bonds, YH XH A, both become stron-ger. The effect is often called -bond cooperativity,[6] sincethe charges flow through the XH bonds, but the termspolarization-enhanced hydrogen bonding[110] or polariza-tion-assisted hydrogen bonding (as opposed to resonance-assisted hydrogen bonding)[46] have also been proposed.Model calculations on moderate strength hydrogen bondsyield typical energy gains of around 20% relative to isolatedinteractions.[7]

-Bond cooperativity drives the clustering of polar groups.In the condensed phases, this leads to formation of XH XH XH chains and rings, in particular for XO, but alsofor XN or S. If double donors (such as H2O) and/or doubleacceptors are involved, they can interconnect chains and ringsto form complex networks. The topology of such networks hasbeen documented in great detail for the OH-rich carbohy-drates.[5, 111, 112]

An unusual array cooperative -bond is shown inScheme 10. The polarity of the water molecule is greatlyenhanced by two hydrogen bonds donated to strong OP

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acceptors, so that the acceptedCCH O hydrogen bond be-comes very short, in fact theshortest ever found for an ace-tylenic donor.[113]

4.2. -Bond Cooperativity orResonance-AssistedHydrogen Bonding (RAHB)

XH groups may also bepolarized by charge flowthrough bonds. For example,

an amide NH group becomes a stronger donor if the amideO atom accepts a hydrogen bond, XH OCNH. Thisresults because the zwitterionic resonance form is stabilized(Scheme 11). The same effect occurs in thio- and seleno-amides.[8] Amide units, as a result of their dual donor andacceptor capacity, often form hydrogen-bonded chains orrings (such as in protein secondary structure; Scheme 12).Since the polarization occurs through bonds, the effect isoften called -bond cooperativity.[6]

XN H

XN H

X = O, S, Se+

_

Scheme 11. Resonance forms of amide, thioamide, and selenoamidegroups. The neutral form is always dominating, but the weight of thezwitterionic form is increased by accepted as well as by donated hydrogenbonds.

XN H X

N H

N

X N

XH

H

X = O, S, Se

Scheme 12. Chains and rings as formed by amides, thioamides, andselenoamides through the -bond cooperativity.

On the basis of studies of intramolecular hydrogen bonds in-diketone enolates Gilli et al. call this effect resonance-assisted hydrogen bonding (RAHB).[114] A short hydrogenbond in the -diketone enolates is associated with a chargeflow through the system of conjugated double bonds(Scheme 13). The CO and CC bonds gain partial doublebond character and are shortened, whereas the CO and CC

bonds are weakened correspondingly. If adelocalization parameter Q (d1 d4)(d3 d2) is plotted against the O Odistance (Figure 22) it is seen that thedelocalization systematically increaseswith a shortening of the hydrogen bondlength. In the extreme case of a symmetricposition of the H atom, Q is zero and theentire fragment becomes symmetric.Completely analogous effects operate in

Figure 22. Resonance-assisted hydrogen bonding (RAHB) in enolonesaccording to Gilli et al.[114] The parameter Q measuring the degree of delocalization decreases with decreasing O O distance (Q 0 indicatesa completely delocalized system). Stars represent intramolecular, andsquares represent intermolecular hydrogen bonds.

longer chains of conjugated double bonds with intra- and alsointermolecular hydrogen bonds.[115] The best known exampleis the carboxylic acid dimer (Scheme 7). Any other suitabledonor acceptor pair connected by a resonant system willalso show the effect. The cases NH O and OH N,[116]NH S/Se,[8] OH S,[117] and SH S[118] (Schemes 12and 14) illustrate the variety, for which experimental evidenceof the -bond cooperativity is available.

O NH

O SH

PS

S S

SP

H

HScheme 14. Examples of -bond cooperative (or resonance-assisted)hydrogen bonds other than OH O. Further examples are given inScheme 12.

4.3. Anticooperativity

Hydrogen bonds may not only enhance, but also reduce thestrengths of each other. This occurs, for instance, at doubleacceptors where two roughly parallel donor dipoles repel eachother (Scheme 15). This effect is probably responsible for thepreferences of homodromic over antidromic cycles of

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C C H OH

H

O

O

P

P

1.96

Scheme 10. A very shortCCH O hydrogen bond.-Bond coorperativity enhan-ces th