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Lecture Modern Hydrogen Bonding Theory By Gastone Gilli Department of Chemistry and Centre for Structural Diffractomet

23rd E uropean C rystallographic M eeting. 6-11 August 2006 Leuven, Belgium. Lecture Modern Hydrogen Bonding Theory By Gastone Gilli Department of Chemistry and Centre for Structural Diffractometry, University of Ferrara, Italy. The Tale of the Princess of the Hydrogen Bond Theory

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Lecture Modern Hydrogen Bonding Theory By Gastone Gilli Department of Chemistry and Centre for Structural Diffractomet

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  1. 23rd EuropeanCrystallographicMeeting 6-11 August 2006 Leuven, Belgium Lecture Modern Hydrogen Bonding Theory By Gastone Gilli Department of Chemistry and Centre for Structural Diffractometry, University of Ferrara, Italy

  2. The Tale of the Princess of the Hydrogen Bond Theory The HB story begins in 1920. It has not been a season of peaceful advancement of sciences but rather a perpetual and sometimes bitter dispute among partisan groups of spectroscopists, thermodynamics, crystallographers and theoreticians. I find more elegant to look at it as a fairy tale, the tale of the beautiful and gifted Princess of the HB Theory who was born in a wonderful palace of white marbles over the Great Sea, full of great savants who dedicated themselves to enlighten the life of men making light where before there was darkness. In her first years of life, she enlightened the world with the treasures of her wisdom disclosing the secrets of ice and water and of the molecules of life. When she was twenty, however, a terrible war devastated the world and, after it, nothing was longer the same. The business people took the place of the enlightened people, new discoveries became to be sold for money as Patents. The white palace was deserted and abandoned and finally occupied by the merciless tribe of the Advanced Technologists. The princess fled, with a small group of Physicochemical Followers, to the Highlands of Crystallography where all was dazzling white and frozen and everything transformed into beautiful crystals. There they remained more than twenty years pursuing their aims in the bright light of the high mountains. This lecture is a kind of Return Tale, telling us how the princess came back to the plain and rebuilt her white palace among the people loosing, however, the clear light of the heights.

  3. The Birth of the HB The idea of HB was firstly conceived in the laboratory of Gilbert Newton Lewis at the end of the ‘20ties while he was writing his famous bookValence and the structure of atoms and molecules (1923). The final assessment of the HB concept is accredited to M.L. Huggins and, independently, to W.M. Latimer and W.H. Rodebush, three young men working there. The first paper published on the HB was: W.M. Latimer and W.H. Rodebush.Polarity and ionization from the standpoint of the Lewis theory of valence.J Am Chem Soc 42: 1419-1433, 1920. The first book on the HB was written by Pauling who made eventually known the HB to the wider chemical community: Pauling, L.The Nature of the chemical bond and the structure of molecules and crystals. An introduction to modern structural chemistry. Cornell University Press, Ithaca, N.Y., 1939, 1940, 1960, Chapter 12, 55 pages. The definition of HB has remained substantially unchanged from then on. I prefer that proposed by: Vinogradov, S.N. and Linnel, R.H.Hydrogen bonding. Van Nostrand-Reinhold, New York, 1971.

  4. The Hydrogen Bond Definition Three-Center-Four-Electron Interaction R-D·-·H . . . . :A-R’ where D is the HB Donor{An electronegative atom such as F, O, N, C, S, Cl, Br, I} and :A the HB Acceptor or Lone Pair Carrier{A second electronegative atom or a multiple bond, that isp-bond} Alternatively: a proton sharing two lone electron pairs from two adjacent electronegative atoms R-D-: . . . H+ . . . :A-R’ Two Very Important HB Properties The HB acceptor is not an atom but a lone electron pair located on that atom Being both D and A electronegative, the HB must have a fixed polarity R-d-D-Hd+. . . .:Ad--R’

  5. Electrostatic and Covalent HBs: The Pauling’s Model Linus Pauling (The Nature of the Chemical Bond, 1939, 1940, 1960)describes two distinct classes of HBs:  Weak and dissymmetric HBs of electrostatic nature: "It is recognized that the hydrogen atom, with only one stable orbital (the 1s orbital), can form only one covalent bond, that the hydrogen bond is largely ionic in character, and that it is formed only between the most electronegative atoms." (HB Chapter - Page 1) Strong and symmetric HBs of covalent nature: These “are exceptions”described as: “. . . the hydrogen bond in the [HF2]- ion lies midway the two fluorine atoms and may be considered to form a half-bond with each.”(HB Chapter - Page 49) [F..H..F]- [O..H..O]-[O..H..O]+ [O..H..O]+

  6. Coulson’s VB Treatment (The Standard HB Model) Pauling’s ideas acquired theoretical dignity with the VB treatment of Coulson and Danielsson in 1954 where the O-H...O bond is described as a mixture of three main VB forms, two covalent and one ionic. This line of thought was embraced by Pimentel and McClellan in their famous book The Hydrogen Bond(1960). They write: “At the 1957 Ljubljana Conferenceone of the important points of fairly general accord was that the electro-static model does not account for all of the phenomena associated with H bond formation”.

  7. The Birth of the Simple Electrostatic Paradigm For reasons difficult to understand, the Standard HB Model was abandoned in the mid-‘60ies and the HB became the weak electrostatic interaction of some 4-6 kcal mol-1 everyone has heard of while strong HBs just disappeared from the chemical horizon. From there on, the HB was divided between a small group of specialists (who still believed in the Standard Model) and the great majority of other scientists (who trusted more the much simpler Electrostatic Paradigm). The effect on HB studies was disastrous and it took more than twenty years to put it right. Why Pauling’s Thought was Abandoned  Weak electrostatic HBs are quoted on page 1 and strong covalent ones at page 49. Since most people read only the first few pages …….  On page 50, strong HBs are defined “exceptions”. Most readers may have thought: Why to bother about exceptions when there are already so many regular HBs to bother about? These are things for specialists!  In VB terms, “the hydrogen atom ... can form only one covalent bond…” does not mean that there is only one bondbut that there may be any combination of two bonds whose bond orders sum up to one, from 1+0 to 0+1 through ½+ ½. Probably very few people understood that correctly!

  8. Another Unsolved Problem: The HB Puzzle Bond lengths and energies of normal chemical bonds are found to depend on the nature of the interacting atoms and are weakly perturbed by their external environment. Conversely, binding energies (EHB) and D···A distances (dD···A) of D-H···:A bonds do not simply depend on the donor (D) and acceptor (:A) nature but show very large variations even for the same donor-acceptor couple. This is what we have called, for the sake of brevity, the HB Puzzle. An extreme example of this behavior comes from the effects produced on the O-H···O bond by the changing acid-base properties of its environment. The weak HO-H···OH2 bond in water [EHB»5 kcal mol-1; dO···O»2.70-2.75 Å] is switched, in acidic or basic medium, to the very strong [H2O···H···OH2]+ or [HO···H···OH]- bonds with EHB up to 30-31 kcal mol-1 and dO···O down to 2.38-2.42 Å.

  9. How to Solve the HB Puzzle: the Problem of the Driving Variable The Electrostatic Paradigm cannot explain the HB Puzzle. Neither the Standard Model provides a full interpretation of it because, while it can explain what covalent and electrostatic HBs are, it cannot suggest which circumstances can produce them. To put the problem in more general terms, there are dozens of physicochemical variables commonly measured in connection with the HB (energies, geometries, IR frequencies, NMR chemical shifts, NQR couplings, and isotopic effects of the HB itself and, in addiction, a large number of other properties of the interacting molecules) and most, if not all, appear to be strongly inter-correlated. But, what’s the driving variable? what’s the variable which, among the many intercorrelated ones, drives the transformation from weak and electrostatic to strong and covalent HB?

  10. A Proposal: The PA/pKa Equalization Principle Two very similar proposals come from early thermodynamic or spectroscopic investigations and are both centered on the matching of the acid-base properties of the HB donor and acceptors moieties, what we like too call, for the sake of brevity, the PA/pKa Equalization Principle. With reference to any generic D-H···:A bond, this principle states that the HB becomes the stronger the smaller is the difference of the donor-acceptor proton affinities: DPA = PA(D-) - PA(A)* or acidic constants: DpKa = pKAH(D-H) - pKBH+(A-H+)* ------------------------------------------------------------------------------------------------------------------------- * Ault, B.S. and Pimentel, G.G. (1975). J. Phys. Chem. 79, 615. * Huyskens, P.L. and Zeegers-Huyskens Th. (1964).J. Chim. Phys. Phys.- Chim. Biol. 61, 81.

  11. Our First Steps in the HB Field As usual, we entered the field by chance. In 1985, we were studying the ligands of the benzadiazepine membrane receptor. One of these ligands was CGS8216 where we noticed something strange: a rather short N-H…O bond of 2.694 Å associated with an interleaving β-enaminone …O=C-C=C-NH… fragment which was almost completely π-delocalized. It was the first indication of a possible correlation between p-delocalization and H-bond strength- what was called a few years later the Resonance-Assisted H-Bond (RAHB) (Gilli, Bellucci, Ferretti & Bertolasi, JACS, 1989; Bertolasi, Gilli, Ferretti & Gilli, JACS, 1991). Since, at the time, few b-enaminones were known, the work started on the analogous class of b-enolones(orb-diketone enols) which were already known to give strong O-H...O bonds through the equally resonant ...O=C-C=C-OH... fragment.

  12. The Development of the O-H····O RAHB

  13. The O-H····O RAHBs Very interesting Class of Strong HBs Different lengths of the resonant spacer Rn (n = 1, 3, 5, 7) The HBs formed were all much stronger than normal (non-resonant) O-H····O bonds, with d(O...O)INTRA = 2.39-2.55 Å d(O...O)INTER = 2.46-2.65 Å

  14. A Model for RAHB: Electrostatic or Covalent? A RAHB Electrostatic Model A RAHB Covalent Model At first (JACS 1989) we suggested a RAHB Electrostatic Model but it became rapidly evident that an efficient RAHB treatment would require a Covalent Model. All hell broke loose because, as we discovered with surprise, the concept itself of covalent HB had been banned some twenty years before and substituted by the acritical but more comfortable Simple Electrostatic Paradigm. RAHB seriously risked to became a kind of bizarre covalent hypothesis. I must thank George A. Jeffrey, with his inimitable unbiased and skeptical style, if RAHB was not immediately cast aside by the scientific establishment but started to be quoted in important books and reviews during the ‘90ties.

  15. Starting Again: The Purely Empirical Approach Fortunately, we were realistic enough not to try to confute the Electrostatic Paradigm. On the other hand,it was perfectly useless because too deeply rooted in the Weltanschaung of so many important and self-confident scientists. I have already given a short critical account of the very nature of these scientific paradigms at the ECM-2000 of Nancy, based on the ideas of Thomas S. Kuhn (The Structure of Scientific Revolutions, The University of Chicago, 1962 and 1970). Anyway, to get out of this impasse, at the beginning of 1993 we decided to change approach and to restartto investigate the O-H...O bond problem from the very beginning by adopting a purely empirical strategy: (i) suspend any previous ideas on the electrostatic or covalent nature of the HB; (ii) define the O-H···O bond as a simple topological structure where a H atom is connected to two or more oxygen atoms; (iii) collect all crystal structures having O-H···O bonds with d(O···O)2.70 Å; (iv) collect all available IR n(O-H) and NMR d(H) data of H-bonded protons; (v) collect all available HB energy data from thermodynamic measurements in gas phase and non-polar solvents; (vi) try to infer a conclusion on the very nature of the O-H···O bond from the ensembleof the data collected.

  16. A Full Classification of Strong HBs

  17. The Five HB Chemical Leitmotifs (CLs) CHARGE - ASSISTED HBs CL # 1: (+/–)CAHB ÞSHB, VSHB Double Charge-Assisted HB Direct Acid-Base PA/pKa Matching CL # 2:(–)CAHB Þ SHB, VSHB Negative Charge-Assisted HB Acid-Base PA/pKa Matching by Proton Loss CL # 3:(+)CAHB Þ SHB, VSHB Positive Charge-Assisted HB Acid-Base PA/pKa Matching by Proton Gain S/P-BOND POLARIZATION - ASSISTED HBs CL # 4: RAHBÞSHB, VSHB Resonance-Assisted or p-Cooperative HB PA/pKa Matching by p-Conjugated-Bond Polarization CL # 5: PAHB Þ MHB Polarization-Assisted or s-Cooperative HB (Partial) PA/pKa Matching by s-Bond Polarization

  18. The Five HB Chemical Leitmotifs (CLs) The most interesting aspect of a HB classification based on HB strengthis that strong HBs belong only to a small number of chemical schemes that we have called Chemical Leitmotifs. The Alchemic Piper plays the Five Magic Tunes that make any Hydrogen Bond stronger: The Chemical Leitmotifs

  19. Symmetry and Covalency (1) The covalent nature of the strong O-H···O bond was assessed by interpreting the experimental results in terms of the Coulson’s VB formalism. We cannot measure covalencybut can evaluate molecular symmetry, the Coulson’s model being the algorithm able to translate one concept into the other. In fact, total symmetry across the HB implies energy equivalence between the twocovalent VB forms, i.e. E(ΨCOV1)=E(ΨCOV2), which is just the situation associated with formation of the covalent HB.

  20. Symmetry and Covalency (2)

  21. The Origin of the Chemical Leitmotifs: The PA/pKa Equalization Principle Chemical Leitmotif # 1: (+/-)CAHB Double Charge-Assisted HB Direct Acid-Base PA/pKa Matching R-1/2-D....H+....A1/2--R The role played by the PA/pKa equalization in HB strengthening is self-evident for the (+/-)CAHB chemical leitmotif R-D-H....:A-R’  R-1/2-D...H+...A1/2--R’  R--D:....H-A+-R’ which collects, by definition, all strong HBs formed by the acid-base pairs with a pKa matching within, say, –3 ÷ 3 DpKa units.     But what about the other leitmotifs? Can we prove that all chemical leitmotifs are simple artifices that molecules can use to obliterate the normally very large DpKa between HB donor and acceptor atoms ?

  22. The Origin of the Chemical Leitmotifs: The PA/pKa Equalization Principle Chemical Leitmotif # 2: (-)CAHB Negative Charge-Assisted HB Acid-Base PA/pKa Matching by Proton Loss [R-D....H....A-R]- Chemical Leitmotif # 3: (+)CAHB Positive Charge-Assisted HB Acid-Base PA/pKa Matching by Proton Gain [R-D....H....A-R]+

  23. The Origin of the Chemical Leitmotifs: The PA/pKa Equalization Principle Chemical Leitmotif # 4: RAHB Resonance-Assisted or p-Bond Cooperative HB PA/pKa Matching by p-Conjugated-Bond Polarization R-D-H...A=RÛR=D...H-A-R

  24. The HB Empirical Rules The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model; Gilli & Gilli, J. Mol. Struct., 2000) and can be summarized as follows:  Any given D-H...A system may form HBs in a wide range of strengths, lengths, symmetries and proton locations, the two extremes being represented by the weak, long, dissymmetric and proton-out-centred HBof electrostatic nature and by the very strong, very short, symmetric and proton-centred HB classifiable as a true 3-center-4-electron covalent bond.  The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to thedifference between the Proton Affinities (DPA) or related Acid-Base Dissociation Constants (DpKa) of the Donor and Acceptor moieties. These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification.

  25. Provisional Conclusions and New Controls We have so far established a sound set of empirical rules which include: A full classification of all existing HBs  A full classification of all strong HBs (The Chemical Leitmotifs)  A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PA/pKa Equalization Principle)  To confirm this last point we have undertaken, two years ago, a new research program aimed at assessing the Full Validity of the PA/pKa Equalization Principle by comparing extended tables of pKa values arranged for chemical classes with the corresponding CSD-derived HB geometries. Hundreds of pKa were collected and more than 11,000 crystal structures examined.

  26. The pKa Slide Rule It is a tool for the graphical evaluation of the difference DpKa = pKAH(D-H) - pKBH+(A-H+) HB Acceptors on the left and HB Donors on the right. pKa values given for chemical class. Results expected: ΔpKa>>0: D-H····A, weak & neutral ΔpKa ≈ 0: D···H···A, strong & centered ΔpKa <<0:-D····H-A+, weak & charged pKa ranges of organic compounds: C-H acids -11 <pKa< 53 Other Donors -1 <pKa< 40 Acceptors -12 <pKa< 16 All -15 <pKa< 53 Water 0 <pKa< 14

  27. Chemical Leitmotifs and PA/pKa Equalization Rules RAHB:RAHB cannot be treated by pKa equalization methods because π-delocalization modifies the pKa’s of the donor and acceptor moieties. (+/-)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor) R–D–H....:A–R’  R–1/2-D...H+...A1/2––R’  R–-D:....H–A+–R’. ΔpKa = pKAH(R-D-H) - pKBH+(R’-A:) (-)CAHB is a proton sharing between two acids (HB donors) R–D–H....:D’–-R’  [R-D...H...D’-R’]- R--D:....H-D’-R’ ΔpKa= pKAH(R-D-H) - pKAH(R-D-H) (+)CAHB is a proton sharing between two bases (HB acceptors) R-+A-H....:A’-R’  [R-A...H...A’-R’]+  R-A:....H-A’+-R’ ΔpKa = pKBH+(R-A:) - pKBH+(R’-A:’) Whenever (-) and (+)CAHBs are both homonuclear (D = D’ or :A = :A’) and homomolecular (R = R’), the matching condition ΔpKa= 0 will hold irrespective of the actual pKa’s of the two interacting moieties. All HBs formed will be strong!

  28. Some Famous HBs

  29. The N-H···O/O-H···N System over the Full DpKa Range When evaluated from the pKa slide rule, the total pKa range is extremely wide: –30 £ pKa£ 60. So far, we have been able to shown that the pKa equalization rule certainly holds in a restricted interval around zero. The problem is now: Does this rule hold in the full DpKa range? We will try to prove that by a full analysis the N-H···O/O-H···N system. Procedure.  In a first CSD search, functional groups of known pKa value and more frequently implied in N-H···O/O-H···N bonds were identified.  Finally, 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group.  Altogether, 9078 different bonds were analyzed (4364 N-H···O, 2289 O-H···N and 2425 -O···H-N+).  For each bond the N···O distances were evaluated as dN-H + dH-O to account for the N-H-O angle and, for each group, the shortest and average distances [dN···O (min) and dN···O (mean)] were registered. These values were compared (see next slide) with the acid-base features of the donors (pKAH range), acceptors (pKBH+ range), and with their combinations (DpKa range).

  30. DpKaversus HB Geometry Correlation - Conclusions The PA/pKa Equalization Principle is therefore fully confirmed in its two forms: All strong HBs correspond to very small DpKa values  DpKa valuesmodulate the HB strengthover the full DpKa range. These conclusions are of great practical importance in at least two respects:  DpKais definitively established as the driving force which controls the HB strength by modulating the HB covalent contribution; It is definitively established that an accurate analysis of structural crystal data leads to the same conclusions suggested, but never proved on a general base, by thermodynamic and spectroscopic methods References:Huyskens and Zeegers-Huyskens, 1964; Zeegers-Huyskens, 1986, 1988; Ault and Pimentel,1975; Ratajczak and Sobczyk, 1969; Sobczyk et al., 1982; Barnes, 1983; Kebarle et al., 1974-1979; Meot-Ner (Mautner) et al., 1984-1988.

  31. Towards a General HB Theory The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law), that is a great collection of HB experimental data neatly organized in tables which, all together, represent a General Taxonomy of the HB Phenomenon, exactly as the Carl Linnaeus’ classification of plants. A scientific theory is something different : It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines. For instance, the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newton’s classical mechanics. How to make a HB Theory HB Properties = F(HB Driving Variable) where HB Driving Variable = DPA/DpKaandF= Transition-State Theory

  32. The Transition-State HB Theory (Gilli et al., J.A.C.S.,2002, 2005; Gilli et al., J. Mol. Struct.,2006) Though it has taken us more than 12 years to develop it, the basic idea is very simple: Any D–H···A bond can be considered as a chemical reaction which is bimolecular in both directions and proceeds via transition-state (TS) formation A–B + C Û A···B···C Û A + B–C D–H···A Û D···H···A Û D···H–A Changes of nomenclature: Reaction PathwayÞPT-Pathway Activation Energy, D‡EÞ PT-Barrier Reaction Energy, DErÞDPA/DpKa Transition State (TS)ÞPT-TS Reaction Coordinate Þ RC=[d(D-H)–d(A-H)] Experimentals: Variable-Temperature X-allography Calculations: DFT-Emulated PT-Pathways Interpretation: Marcus Rate-Equilibrium Theory; Leffler-Hammond Postulate

  33. Acknowledgments I have to thank my direct coworkers, without whose help this work could have not been accomplished Valerio BERTOLASI Paola GILLI Valeria FERRETTI Loretta PRETTO and the scientific institutions which made available to us the databases without which this work could not even be started NIST National Institute of Standards and Technology for the use of the NIST Chemistry WebBook CCDC Cambridge Crystallographic Data Centre for the use of the Cambridge Structural Database

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