University of Ferrara Department of Chemistry and Centre for Structural Diffractometry

1. Intermolecular Interactions and Molecular Recognition Przesieka, 8-12 June 2010 The Dual H-bond as a Chemical Reaction. A Basis for a Comprehensive H-bond Theory Paola Gilli University of Ferrara Department of Chemistry and Centre for Structural Diffractometry

2. The topics of the present lecture have been previously presented to other meetings and, in particular, to: ISIC-12 XII International Seminar on Inclusion Compounds Stellenbosh, South Africa, 4-9 April 2009 Ab Initio Prediction of H-Bond Energies and/or Geometries Paola Gilli H2 BR XVIII International Conference on "Horizons in Hydrogen Bond Research" Paris, 14-18 September 2009 The Nature of the Hydrogen Bond: Models and Theories Paola Gilli

3. H-Bond: Classical Definitions Three-Center-Four-Electron Interaction R-D·-·H · · · · :A-R’ where Dis theProton Donor{an electronegative atom such as F, O, N, C, S, Cl, Br, I} and :A the Proton AcceptororElectron-Pair Carrier{a second electronegative atom or the p-bond of a multiple bond} Otherwise: a proton sharing two electron pairs coming from two adjacent electronegative atoms R-D-: · · · H+ · · · :A-R’ This second formulation makes clear that: · Both donor and acceptor electronegativities, c(D) and c(A), must be greater than that of the central hydrogen, c(H); · Any H-bond will be the stronger the greater the donor/acceptor electronegativies (that is their affinities for the proton) are; · Both D-: and :A must be bases, so introducing the use of acid-base quantities {gas-phase proton affinities [PA(D-) and PA(A)] or water acid-base dissociation constants [pKAH(D-H) and pKBH+(A-H+)]} in any H-bond treatment.

4. Some Basic References 1. W.M. Latimer, W.H. Rodebush, J. Am. Chem. Soc. 42: 1419-1433 (1920). 2. L. Pauling, The Nature of the Chemical Bond (Cornell University Press, Ithaca, NY, 1960) 3. G.C. Pimentel, A.L. McClellan, The Hydrogen Bond (Freeman: San Francisco, 1960). 4. S.N. Vinogradov, R.H. Linnel, Hydrogen Bonding (Van Nostrand Reinhold: New York, 1971). 5. G.A. Jeffrey, An Introduction to Hydrogen Bonding (Oxford University Press: Oxford, 1997). 6. G. Gilli, P. Gilli, The Nature of the Hydrogen Bond. Outline of a Comprehensive Hydrogen Bond Theory (Oxford University Press: Oxford, 2009). 7. P. Gilli, L. Pretto, V. Bertolasi, G. Gilli, Predicting H-bond strengths from acid-base molecular properties. ….Acc. Chem. Res. 42: 33-44 (2009). 8. P. Gilli, G. Gilli, H-bond models and theories: The dual H-bond model and its properties.J. Mol. Struct. 972: 2-10 (2010).

5. The H-Bond Strength The outstanding H-bond property is the H-bond strength, quantified as ·H-bond-dissociation energy, EHB, or ·H-bond-dissociation enthalpy, DHDIS, but often monitored by ·the D···A contact distance, dD···A, or ·the sum d’D···A= dD-H + dH···A, a quantity naturally accounting for D-H-A angle changes. Empirically, energies and geometries are found to be interrelated and encompassed between two extremes: (i)weak, long, dissymmetric, proton-off-centered, and mostly bent D-H···:A bonds of electrostatic nature; and (ii)strong, short, symmetric, proton-centered, and linear D···H···A bonds reducible to three-centre-four-electron interactions of covalent nature.

6. Predicting H-Bond Strengths: The H-Bond Puzzle Unlike normal chemical bonds, H-bonds feature properties that do not simply depend on the donor/acceptor nature but undergo large variations even for a same donor-acceptor couple. For example, weak HO-H···OH2 bonds in neutral water [EHB » 5 kcal mol-1; dO···O » 2.70-2.75 Å] change, in acidic and basic medium, to the very strong [H2O···H···OH2]+ or [HO···H···OH]- bonds having EHB » 26-31 kcal mol-1 and dO···O » 2.38-2.42 Å. This surprising behavior, that we have called the H-bond puzzle, practically prevents prediction of H-bond strengths from molecular properties. The present communication will try to solve the puzzle by re-examining the problem and discussing the most recent methods developed to make such strength predictions feasible.

7. Early Models for a Comprehensive H-Bond Theory Rather incredibly, no general model able to rationalize H-bond behavior over the full range of H-bond energies (0 ≤ EHB ≤ 45 kcal mol-1) has ever been attempted, till very recently. Practically, all early interpretations neglect strong H-bonds and remain confined to the rather weak ones, on the ground of the following paradoxical considerations: ·Since strong H-bonds are quite rare (at least at the age), they are “exceptions” which “can be reasonably neglected in the treatment of the much more copious H-bonds of normal strength” (Pauling, The Nature of the Chemical Bond, 1939, 1940, 1960); ·“If we discount such exceptions, hydrogen bonding may be quite well understood at a qualitative level using simple electrostatic models.” (Coulson, as reported by McWeeny in Coulson’s Valence, 1979). ·This is the origin of the well known Simple Electrostatic Model (SEM) for which H-bonded molecules can be suitably modeled by a small number of positive and negative point charges or multipoles variously combined with 6-exp or 6-12 atom-atom potentials. ·The first to re-examine critically SEM was, once more, Coulson who, around 1954, suggested an essential covalent contribution also to moderately strong H-bonds, so reinventing what we shall later call the Electrostatic-Covalent H-Bond Model (ECHBM). ·The damage was however done! The imaginative idea of a purely electrostatic H-bond was born, leaving ECHBM confined to a restricted number of specialists, until it was revived by us in 1994 (Covalent nature of the strong homonuclear H-bond…, Gilli et al., JACS, 1994).

8. A New Comprehensive H-Bond Model: The Dual H-Bond The clue of the problem is that the H-bond is not really a bond donated by the donor D-H to the acceptor :A but rather consists of two bonds formed by a same proton with two acceptors, each carrying an electron pair. In chemical words, the H-bond is not a reaction of nucleophilic addition but rather of nucleophilic substitution along the bimolecular proton-transfer (PT) reaction pathway leading from D-H···A to D···H-A through the D···H···A transition state. Hence, what we are used to call H-bond is actuallya minimum (or two minima) along this reaction pathwaywhich may have quitedifferent shapes according to the strength of the H-bond formed.

9. The Dual H-Bond (continued) D–H···A Û D···H···A Û D···H–A The possible shapes the PT reaction pathway may adopt according to the different strength of the H-bond formed are essentially of three types: (i) only one accessible asymmetric single well (aSW) inweak bonds; (ii) two symmetric or slightly asymmetric double wells (sDW, saDW) in strong bonds (also called LBHBs = low-barrier H-bonds); or (iii) one symmetric single well (sSW) in very strong bonds. Weak HB (aSW) Moderately Strong HB (saDW) Strong HB (sDW) (LBHB) Very Strong HB (sSW)

10. The Dual H-Bond Energy According to the dual H-bond model,the H-bond energy, EHB, is not properly the D-H···:A dissociation energy, but rather the smaller of the two bond-dissociation energies, D0(D-H) and D0(H-A), by which D- and :A are competitively bound to the same central proton. If one is stronger, the other is weaker, and weak the overall H-bond will be. Strong bonds will occur only when DD0= D0(D-H) -D0(H-A) = 0 or, in terms of affinity for the proton (pa), when Dpa = pa(D-) - pa(:A) = 0. These relationships, when expressed as DPA = PA(D-) - PA(:A) (in the gas phase) or DpKa= pKAH(D-H) - pKBH+(A-H+) (in condensed phase), assume the name of PA/pKa equalization principle. Crystal and thermodynamic data show that the condition DD0= Dpa  0 typical of strong H-bonds can be achieved onlyin specific chemical circumstances, normally indicated as the four strong H-bond chemical leitmotifs.

11. A Library of Strong H-bonds: The Chemical Leitmotifs (CLs) CHARGE-ASSISTED H-BONDs CL # 1: (±)CAHB ÞS, VS Double Charge-Assisted HB Acid and base having by chance the same PA/pKa CL # 2:(–)CAHB Þ S, VS Negative Charge-Assisted HB Two acids having lost a proton (same PA/pKa) CL # 3:(+)CAHB Þ S, VS Positive Charge-Assisted HB Two bases having gained a proton (same PA/pKa) S= Strong, VS= Very Strong, M= Medium Strong, W= Weak H-Bond s/p-BOND COOPERATIVE H-BONDs CL # 4: RAHBÞS, VS Resonance-Assisted HB or p-Cooperative HB PA/pKa Matching by p-Conjugated-Bond Polarization CL # 5: PAHB Þ M Polarization-Assisted HB or s-Cooperative HB (Partial) PA/pKa Matching by s-Bond Polarization NEITHER CHARGE- NORRESONANCE/POLARIZATION - ASSISTED H-BONDs CL # 6:OHBÞW Ordinary HB No PA/pKa Matching

12. Towards a comprehensive H-bond theory: Driving variables and H-bond theories Any generic H-bond theory can be written as H-Bond Properties = F {H-Bond Driving Variables}, where F is a theoretical operator transforming variables into properties, such as H-bond geometries, energies, PT barriers, dipole moments, IR frequencies, NMR chemical shifts, etc. Following the dual H-bond logic, the driving variables can be traced back to two proton affinities, pa(D-) and pa(:A), or better to their linear combinations, sum[Spa]and difference [Dpa],which are the only quantities to have a clear physical meaning. The eq above becomes H-Bond Properties = F {[Spa = pa(D-) + pa(:A)];[Dpa = pa(D-) - pa(:A)]} where Sum = Spa≈ [χ(D)+ χ(A)]/2 = Average electronegativity of D and A Difference = Dpa= Reaction energy, DrE, or any of its LFER-related quantities (DPA, DpKa) This equation will be now analyzed for two special cases: (1) Spa variable for Dpa = 0; and (2) Dpa variable for Spa = constant.

13. Case study 1. pa variable for pa= 0: 1.1 The Importance of Electronegativity H-Bond Properties = F {[Spa = pa(D-) + pa(:A)];[Dpa= 0]} Homomolecular (-)CAHBs and (+)CAHBs of the type [X···H···X]- (X = F, O, Cl, N, Br, S) and [X···H···X]+ (X = O, N) are couples of two identical acids or bases which have Dpa= 0 by definition, and whose energy, EHB, then corresponds to the maximum energy EHB,MAX (X···X). This EHB,MAX quantity plays an important role in H-bond theories, because a small number of very accurate EHB,MAXvalues can be obtained from the NIST database as gas-phase dissociation enthalpies, DHDIS, of simple X···H···X homomolecular complexes and then directly correlated with the corresponding X-Hbond-dissociation energies, D0(X-H).

14. Case study 1. pa variable for pa= 0 (continued): 1.2 The Importance of Electronegativity The following regression equation is obtained EHB,MAX DHDIS(Dpa= 0) = -31.3 + 0.55 D0(X-H) (kcal mol-1; r =0.900, n =8) which shows that maximum H-bond energies are proportional to one half of the X-H bond-dissociation energies, in complete agreement with the VB concept that strong H-bonds are three-centre-four-electron covalent interactions splitting a single bond in two half bonds with bond numbers n = 1/2. Now, since D0(X-H) and the Pauling’s electronegativity cP(X) are linearly related D0(X-H) = -18.2 + 37.4 cP(X) (kcal mol-1; r =0.956, n =8), we obtain the final equation EHB,MAX DHDIS(Dpa= 0) = -44.8 + 21.6 cP(X) (kcal mol-1; r =0.907, n =8), showing, for the first time in the history of the H-bond, that the maximum energy achievable for any given X···H···X bond is a linear function of c(X), the electronegativity of X.

15. Case study 1. pa variable for pa= 0 (continued): 1.3 H-Bond Electronegativity Classes, EC(D,A) In Summary: · There may not be a unique energy scale for all H-bonds; · For any generic D-H···:A bond, any different (D,A) couple will generate its own specific H-bond electronegativity class, EC(D,A); ·Each class will be fully characterized by a specific couple of linearly related values, that is [EHB,MAX(D···A) / Sc(D,A)]. A Quite Useful Energy-Geometry Relationship It has been recently shown by semiempirical methods (Gilli et al., Acc Chem Res 2009) that all bonds belonging to a same EC(D,A)are characterized by well-definite ranges of energies and D···A distances, which are mutually related by the exponential equation EHB = EHB,MAX exp[-k(d’D···A -d’D···A,min)] where EHB,MAX is the maximum energy associated with the minimum d’D···A,mindistance, and k an empirical constant ranging from 5 to 7. The Next Figure displays the general correlation for all EC(D,A)’s for which sufficient data are available.

16. EHB = EHB,MAX exp[-k (d’D···A-d’D···A,min)] EHB EC(F,F) EC(Cl,Cl) EC(Br,Br) d’D···A EC(O,O) EC(N,O) EC(N,N) EC(S,S) EHB d’D···A The general correlation for all EC(D,A)’s for which sufficient data are available ·The different colors of curves and horizontal lines indicate the different EC(D,A)’s ·Six are homonuclear and just one heteronuclear (N–H···O/O-H···N)

17. EHB = 32.0 exp[-5.1(d’D···A- 2.360)] (red figures set for theO–H···O bond) Let’s take the homonuclear O–H···O bond as an example: The red horizontal line indicates the full range ofO···O distances ever found, from the longest distance corresponding to the sum of the vdW radii (3.70 Å for EHB set to zero) to the shortest one of2.36 Å observed in the [H2O···H···OH2]+ water complex having EHB,MAX= 32.0 kcal mol-1 The red curve corresponds to the exponential equation above. It is seen to fit well the experimental points, that is the four EHB/ d’D···A couples measured for the neutral (OHB) and the three charge-assisted (CAHB) bonds marked in the legend

18. Case study 2. Dpa variable for Spa= constant: The PA/pKa Equalization Principle H-bond Properties = F {[Spa= constant]; [Dpa= pa(D-)-pa(:A)]} For a given EC(D,A), Spa is a constant, so that the H-bond properties depend only on the difference Dpa, where the nature of pa(D-) and pa(:A) depends, in turn, on the choice of F. We have already described three different but interconsistent models (or theories): (i) In theelectrostatic-covalent H-bond model (ECHBM), F is the H-bond Coulson’s VB formalism, the duality is expressed by the D–H···A ↔ -D···H–A+ resonance, and Dpa= E[Y(-D···H–A+)]– E[Y(D···H–A)] is the energy difference between the two VB wavefunctions. (Gilli et al., JACS 1994; for a short review see: Gilli & Gilli, J. Mol. Struct. 2000). (ii) In the transition-state H-bond theory (TSHBT), F is the traditional TST, the duality arises from the tautomeric D–H···A Û D···H···A Û D···H–A equilibrium, and Dpa is the classical reaction energy DrE = E(D–H···A ) -E(D···H–A). (Gilli et al., JACS 2002, 2005; for a short review see: Gilli et al., J. Mol. Struct. 2006). (iii) Finally, the PA/pKa equalization principle (rooted in the seminal papers by Huyskens, Zeegers-Huyskens, Pimentel, Sobczyk, Kebarle & Mautner) represents a TSHBT version where DrE is empirically evaluated by LFER-related quantities, in particular: · the donor/acceptor acid-base parameters PA and pKa, so that Dpa can be identified with DPA= PA(D-) - PA(:A) in the gas phase or DpKa= pKAH(D-H) - pKBH+(A-H+) in condensed phase (Gilli et al., Acc. Chem. Res. 2009; for a short review see: Gilli & Gilli, J. Mol. Struct. 2010).

19. Practical Evaluation of the H-bond Strength: Predicting H-bond Strengths from Molecular Properties (i) VB methods (ECHBM) are of prevalent theoretical interest. Their main application is the well-known Lippincott & Schroeder method (1955, 1957) which, however, does not predict H-bond strengths but can calculate them starting from H-bond geometries; (ii) TSHBT needs DrE evaluation by complex QM simulations of PT pathways and their interpretation in terms of the Marcus’ rate-equilibrium theory; (iii) conversely, PA/pKa equalization methods are easily accessible if proper advantage is taken of the extensive PA and pKa compilations presently available. PA/pKa equalization methods have been the subject of a recent thermodynamic analysis (Gilli et al., J. Mol. Struct. 2007; Acc. Chem. Res. 2009) which has been able to show that ·DPA parameters can properly treat only (-)CAHBs and (+)CAHBs, while ·DpKa’s are compatible with most H-bonds [OHBs, (±)CAHBs, (-)CAHBs, and (+)CAHBs] · leaving out only RAHBs, whose correct DpKa values cannot be evaluated because of the perturbations induced by the p-delocalization effects. pKa-matching is therefore the method of election for predicting H-bond strengths, provided we are able to collect the pKa(H2O) values of all most common H-bond donors and acceptors, a not simple task because these values span the considerable range -15 £pKa£53. The results of our work in the field have been summarized in form of a bar-chart called the pKa slide rule

20. Practical Evaluation of the H-bond Strength: Preliminary Notes on the Correct Use of the pKa Values The use of the pKa slide rule requires some preliminary comments on the classification of all H-bonds with respect to their acid-base properties: ·OHBs and (±)CAHBs are proton-transfer H-bondsrelated to the acid-baseequilibrium R–D–H····:A–R’ Û R–1/2-D···H+···A1/2––R’ Û R–-D:····H–A+–R’ and whose properties are fully controlled by the quantity ΔpKa(acid-base)= pKa(acid) - pKa(base) = pKAH(R-D-H) - pKBH+(R’-A-H+) ·· (-)CAHBs and(+)CAHBs are instead proton-sharing H-bonds of two different types: (-)CAHBs are acid-acid equilibria whose proton is shared bytwo H-bond donors (two acids) R1–D1–H····:D2–-R2Û [R1-D1···H···D2-R2]-Û R1--D1:····H-D2-R2 and whose properties are fully controlled by the quantity ΔpKa(acid-acid)= |pKAH(R2-D2-H) - pKAH(R1-D1-H)| (+)CAHBs are base-base equilibria whose proton is shared bytwo H-bond acceptors (two bases) R1-+A1-H····:A2-R2Û [R1-A1···H···A2-R2]+ Û R1-A1:····H-A2+-R2 and whose properties are fully controlled by the quantity ΔpKa(base-base)= |pKBH+(R2-A2-H+) - pKBH+(R1-A1-H+)| ··· To notice that, whenever (-)CAHBsand (+)CAHBs are both homonuclear (D1 = D2 or :A1 = :A2) and homomolecular (R1 = R2), the matching condition ΔpKa= 0 will hold irrespective of the actual pKa of the two interacting moieties

21. The pKa Slide Rule is a tool for fast graphical evaluation of the approximate DpKa differences: DpKa = pKAH (donor) - pKBH+(acceptor) ·Data are arranged in two columns: D-H donors (or A-H acids) on the right, and A: acceptors (or B bases) on the left, ·pKa values are given for chemical classes ·different colors indicate the atoms involved ····· Strong (±)CAHBs occur when an acid and a base lie on a same horizontal line. In general: ΔpKa>>0: D-H····A, weak & neutral ΔpKa ≈ 0: D···H···A, strong & centered ΔpKa <<0:-D····H-A+,weak & charged Strong (-)CAHBs occur when two acids (on the right) lie on a same horizontal line, Strong (+)CAHBs when two bases (on the left) lie on a same horizontal line.

22. The pKa Slide Rule Organic donors (-1£ pKa£40) are shifted in regard to organic acceptors (-12£ pKa£16), so that a large group of acceptors (nitro and carbonyl compounds, nitriles, ethers, alcohols, and sulfoxides) fall in a region facing some inorganic acids but no organic donors and are then expected to form only weak H-bonds with the latter. The same happens for weak donors (amines, anilines, and alcohols) which do not face any known acceptor. Maximum overlap between organic donors and acceptors occurs in the interval 0£ pKa£ 14 where the greatest number of strong H-bonds are expected.

23. Practical Use of the pKa Slide Rule: The Water-Water Dimer · The pKa slide rule can be easily redrawn as a true slide rule by allowing the donor and acceptor scales to shift reciprocally so to bring into coincidence the donor and acceptor molecules. · In this example the slide rule is set in such a way to permit graphical DpKa evaluation and empirical strength appreciation for the O-H···:O bond in the water dimer. DpKa= 17.4 H-Bond Strength = MEDIUM

24. EC(O,O) EC(N,O) EC(N,N) EC(S,S) EHB d’D···A EHB = EHB,MAX exp[-k (d’D···A-d’D···A,min)] Diagnosis for the Water Dimer: d’O···O ≈ 2.70 Å EHB ≈ 5 kcal mol-1

25. Practical Use of the pKa Slide Rule: Urea-Phosphoric Acid DpKa= 2.1 H-Bond Strength = STRONG

26. EC(O,O) EC(N,O) EC(N,N) EC(S,S) EHB d’D···A CRBAMP01: N-100K d’O···O ≈ 2.409 Å EHB = EHB,MAX exp[-k (d’D···A-d’D···A,min)] Diagnosis for Urea-Phosphoric Acid: d’O···O ≈ 2.42 Å EHB ≈ 22 kcal mol-1

27. A Gallery of the Most Famous Strong H-bonds 32.42 12.80 21.39 22.35 (-)CAHB 15.30 23.21 14.99 23.69 12.89 24.50 21.83 22.39 24.80 26.23 23.09 22.17 20.88 22.54 (+)CAHB 20.56 18.29 22.17 24.30 21.39 22.17 9.00 (±)CAHB 12.78 13.87 13.31 13.52 22.17 14.52 23.81 10.87 P. Gilli et al., Acc. Chem. Res. (2009);EHB values (kcal mol-1) calculated by the exponential equation

28. Systematic Applications of the pKa-Equalization Methods: 1. N-H···O/O-H···N Bonds are DpKa-Modulated over the Full pKaRange When evaluated from the pKa slide rule, the total pKa range is enormous:–30 £ pKa£ 65. ·The problem is now: Does DpKa predict H-bond strengths over the full DpKa range? ·To verify this point, we have performed a full analysis of the N-H···O/O-H···N bond system on the Cambridge Structural Database (CSD). Procedure: ·In a first CSD search, the functional groups of known pKa range and most frequently involved in N-H···O/O-H···N interactions were identified. ·Next, 10 classes of donors and 11 of acceptors were selected and the search was restarted for each separate donor-acceptor couple. ·Altogether, 8681 bonds were analyzed (3968 N-H···O, 2295 O-H···N and 2418 -O···H-N+). ·N···O distances were evaluated as d’N···O = dN-H + dH-O to account for N-H-O angle changes and, for each group, minimum and average distances were registered. ·These geometrical values were compared (next slide) with the acid-base features of the donors (pKAH range), of the acceptors (pKBH+ range), and with their combinations (DpKa range).

29. 1. N-H···O/O-H···N Bonds are DpKa-Modulated over the Full pKaRange (Continued) DpKa large & positive HBs weak & neutral HB-strengths Ücolor code HBs weak & charged DpKalarge & negative From: P. Gilli et al., Acc. Chem. Res. 42: 33-44 (2009)

30. 1. N-H···O/O-H···N Bonds are DpKa-Modulated over the Full pKaRange (Continued) All strong H-bonds are located in a same position (orange-red block) associated with complexes of phenols and carboxylic acids with azines, azoles, and second aminic moieties of monoprotonated diamines, which form strong H-bonds because their global ΔpKa range (from 11 to -8) encompasses the zero, and therefore a consistent fraction of them is expected to fall within the interval of true pKa matching. ·To notice that the information obtained is statistical because individual pKa’s are unknown and, accordingly, d’N···O distances can only be compared with the average ΔpKa intervals of each donor-acceptor group. ·Notwithstanding, the many regularities observed definitely support the idea that H-bond strengths are essentially ΔpKa-driven in the complete range of ΔpKa values.

31. 2,6-Dichloro- 4-nitrophenol Pentachlorophenol Picric acid Dichloropicric acid Systematic Applications of the pKa-Equalization Methods: 2.DpKa / EHB / d’D···A Relationships in Nitro- and Halogeno-Phenols A second verification of the complex DpKa / EHB / d’D···A relationships comes from the study of the H-bonds formed by nitro- and halogeno-phenols with various N- and O-bases, a class of compounds with a good pKa matching already studied for many years by the Wroclaw (Sobczyk, Malarski, Lis, Grech, Majersz, Koll, …) and Poznan (Szafran, Dega-Szafran, Katrusiak, …) groups and for which we have recently determined (Gilli, Bertolasi & Gilli) the X-ray structures of 18 new complexes. Hence, this system constitutes a well-documented group of structures where d’D···A values range from 2.40 to 3.55 Å, EHB values (as evaluated by the Lippincott & Schroeder method) from 0.1 to 24 kcal mol-1, and whose thermodynamic pKa parameters are often known with sufficient precision.

32. EHB versus d’D···A Scatterplot in Nitro- and Halogeno-Phenol Complexes with N- and O-Bases ·Open symbols = HBs donated by phenols; Full symbols = HBs accepted by the NO2 groups ·O-H···O bonds are intrinsically stronger than N-H···O ones (different electronegativity class) and the EHBversusd’D···A curve has the expected exponential form discussed above with reasonably similar exponential factor, k. · Let’s see now how these two quantities depend on DpKa.

33. EHB versus DpKa Scatterplot in Nitro- and Halogeno-Phenol Complexes with N- and O-Bases · The EHBversusDpKa curve displays an approximate exponential form, a fact that still awaits theoretical interpretation because it apparently violates the rule that all free-energy relationships should be linear (suggestions from the audience are welcome). · According to the PA/pKa equalization principle, very strong H-bonds are observed only when DpKa is not far from zero. · The dispersion of the data is most probably imputable to uncertainties on the pKa values used.

34. d’D···A versus DpKa Scatterplot in Nitro- and Halogeno-Phenol Complexes with N- and O-Bases · The shape of the d’D···AversusDpKa curve is nearly linear. Also this result is surprising because, in chemistry, all energy-distance relationships should be exponential (help from the audience is still welcome). ·The linearity of the plot, anyway, is rather impressive and can only be interpreted as a substantial confirmation that the H-bond geometry is actually modulated by the DpKa over the full DpKa range.

35. A 3-Dimensional DpKa / EHB / d’D···A Correlation in Nitro- and Halogeno-Phenol Complexes with N- and O-Bases

36. END of LECTURE