Diapositiva 1

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
D is the Proton Donor an electronegative atom
such as F, O, N, C, S, Cl, Br, I and A the
Proton Acceptor or Electron-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 DA contact distance,
dDA, or the sum dDA dD-H dHA, 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-HA bonds of electrostatic
nature and (ii) strong, short, symmetric,
proton-centered, and linear DHA 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-HOH2 bonds in
neutral water EHB 5 kcal mol-1 dOO
2.70-2.75 Å change, in acidic and basic medium,
to the very strong H2OHOH2 or
HOHOH- bonds having EHB 26-31 kcal
mol-1 and dOO 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. Practica
lly, 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 Coulsons 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).
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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-HA to DH-A through the DHA
transition state.
Hence, what we are used to call H-bond is
actually a minimum (or two minima) along this
reaction pathway which may have quite different
shapes according to the strength of the H-bond
formed.
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The Dual H-Bond (continued)
DHA Û DHA Û DHA 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)
in weak 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)
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The Dual H-Bond Energy
According to the dual H-bond model, the H-bond
energy, EHB, is not properly the D-HA
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 only in specific chemical circumstances,
normally indicated as the four strong H-bond
chemical leitmotifs.
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A Library of Strong H-bonds The Chemical
Leitmotifs (CLs)
CHARGE-ASSISTED H-BONDs
CL 1 ()CAHB Þ S, 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 RAHB Þ S, 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- NOR RESONANCE/POLARIZATION -
ASSISTED H-BONDs
CL 6 OHB Þ W Ordinary HB No PA/pKa Matching
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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 ?(D) ?(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.
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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 XHX- (X F, O, Cl, N, Br, S)
and XHX (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
(XX). This EHB,MAX quantity plays an
important role in H-bond theories, because a
small number of very accurate EHB,MAX values can
be obtained from the NIST database as gas-phase
dissociation enthalpies, DHDIS, of simple
XHX homomolecular complexes and then
directly correlated with the corresponding X-H
bond-dissociation energies, D0(X-H).
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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 Paulings 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 XHX bond is a
linear function of c(X), the electronegativity of
X.
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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-HA
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(DA) /
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 DA distances, which are mutually
related by the exponential equation EHB
EHB,MAX exp-k (dDA -?dDA,min) where
EHB,MAX is the maximum energy associated with the
minimum dDA,min distance, 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 (dDA- dDA,min)
EHB
EC(F,F) EC(Cl,Cl) EC(Br,Br)
dDA
EC(O,O) EC(N,O) EC(N,N) EC(S,S)
EHB
dDA
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
(NHO/O-HN)
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EHB 32.0 exp-5.1 (dDA- 2.360) (red
figures set for the OHO bond)
Lets take the homonuclear OHO bond as an
example The red horizontal line indicates the
full range of OO 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 of 2.36 Å observed in the
H2OHOH2 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/ dDA 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 the electrostatic-covalent H-bond model
  (ECHBM), F is the H-bond Coulsons VB formalism,
  the duality is expressed by the DHA ?
  -DHA resonance, and Dpa
• EY(-DHA) EY(DHA) 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 DHA Û DHA
  Û DHA equilibrium, and Dpa is the classical
  reaction energy DrE E(DHA ) - E(DHA).
• (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).

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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 DpKas 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 pKa53. 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-bonds related to the acid-base
equilibrium RDHAR Û
R1/2-DHA1/2R Û R-DHAR and
whose properties are fully controlled by the
quantity ?pKa(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 by two H-bond
donors (two acids) R1D1HD2-R2 Û
R1-D1HD2-R2- Û R1--D1H-D2-R2 and
whose properties are fully controlled by the
quantity ?pKa(acid-acid) pKAH(R2-D2-H) -
pKAH(R1-D1-H)   ()CAHBs are base-base
equilibria whose proton is shared by two H-bond
acceptors (two bases) R1-A1-HA2-R2 Û
R1-A1HA2-R2 Û R1-A1H-A2-R2 and
whose properties are fully controlled by the
quantity ?pKa(base-base) pKBH(R2-A2-H) -
pKBH(R1-A1-H) To notice that,
whenever (-)CAHBs and ()CAHBs are both
homonuclear (D1 D2 or A1 A2) and
homomolecular (R1 R2), the matching condition
?pKa 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 ?pKagtgt0
D-HA, weak neutral ?pKa 0
DHA, strong centered ?pKa
ltlt0-DH-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 pKa40)
are shifted in regard to organic acceptors (-12
pKa16), 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-HO bond in the water dimer.
DpKa 17.4 H-Bond Strength MEDIUM
24
EHB EHB,MAX exp-k (dDA- dDA,min)
Diagnosis for the Water Dimer dOO 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
EHB EHB,MAX exp-k (dDA- dDA,min)
Diagnosis for Urea-Phosphoric Acid dOO
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
22.54
20.88
()CAHB
18.29
20.56
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-HO/O-HN Bonds are
DpKa-Modulated over the Full ?pKa Range
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-HO/O-HN 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-HO/O-HN 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-HO, 2295 O-HN and 2418 -OH-N).
NO distances were evaluated as dNO
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-HO/O-HN Bonds are DpKa-Modulated over
the Full ?pKa Range (Continued)
DpKa large positive
HBs weak neutral
HB-strengths Ü color code
HBs weak charged
DpKa large negative
From P. Gilli et al., Acc. Chem. Res. 42 33-44
(2009)
30
1. N-HO/O-HN Bonds are DpKa-Modulated over
the Full ?pKa Range (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 ?pKa 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 pKas are unknown
and, accordingly, dNO distances can only be
compared with the average ?pKa intervals of each
donor-acceptor group. Notwithstanding, the
many regularities observed definitely support the
idea that H-bond strengths are essentially
?pKa-driven in the complete range of ?pKa values.
31
Systematic Applications of the pKa-Equalization
Methods 2. DpKa / EHB / dDA Relationships in
Nitro- and Halogeno-Phenols
A second verification of the complex DpKa / EHB /
dDA 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 dDA
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 dDA 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-HO bonds are intrinsically stronger than
N-HO ones (different electronegativity class)
and the EHB versus dDA curve has the
expected exponential form discussed above with
reasonably similar exponential factor, k.
Lets 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 EHB versus DpKa 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
dDA versus DpKa Scatterplot in Nitro- and
Halogeno-Phenol Complexes with N- and O-Bases
The shape of the dDA versus DpKa 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 / dDA
Correlation in Nitro- and Halogeno-Phenol
Complexes with N- and O-Bases
36
END of LECTURE