Transcript Diapositiva 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
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
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.
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).
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.
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.
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).
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 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.
The Dual H-Bond (continued)
D–H···A  D···H···A  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) 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)
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 only in specific chemical circumstances, normally indicated as the
four strong H-bond chemical leitmotifs.
A Library of Strong H-bonds: The Chemical Leitmotifs (CLs)
CHARGE-ASSISTED H-BONDs
CL # 1: (±)CAHB  S, VS
Double Charge-Assisted HB
Cl 1/2
Acid and base having by chance the same PA/pKa
CL # 2: (–)CAHB S, VS
Negative Charge-Assisted HB
Two acids having lost a proton (same PA/pKa)
37 1
2 .4 H
O
Cl
Å O
H
Ar
O
Ar
2.37-2.55 Å
DIBENZOYLMETHANE
ENOLS
O
DpKa = -0.70
CH3
PENTACHLOROPHENOL p-TOLUIDINE
R
CARBOXYLIC ACID CARBOXYLATE
S= Strong, VS= Very Strong,
M= Medium Strong, W= Weak
H-Bond
s/p-BOND COOPERATIVE H-BONDs
O
Cl
O
Å
H 2. 430 3 O
H
H
H
O
H
WATER (same PA/pKa)
HYDRONIUM
CL # 3: (+)CAHB S, VS
Positive Charge-Assisted HB
Two bases having gained a proton
R
O
1/2
2.50 H
62 Å N
Cl
Cl
CL # 4: RAHB  S, VS
Resonance-Assisted HB or p-Cooperative HB
O
PA/pKa Matching by p-Conjugated-Bond Polarization
2.7501 Å
O
CL # 5: PAHB  M
Polarization-Assisted HB or s-Cooperative HB
O
O
(Partial) PA/pKa Matching by s-Bond Polarization
O
WATER
NEITHER CHARGE- NOR RESONANCE/POLARIZATION - ASSISTED H-BONDs
CL # 6: OHB  W
Ordinary HB
No PA/pKa Matching
H
D
H
A
D
A
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)
pa(D-)
This equation will be now analyzed
for two special cases:
(1) Spa variable for Dpa = 0; and
(2) Dpa variable for Spa = constant.
Dpa
- pa(A)
Spa
pa(A)
Case study 1. Spa variable for Dpa= 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,MAX values 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-H bond-dissociation energies, D0(X-H).
Case study 1. Spa variable for Dpa= 0 (continued):
EHB,MAX  DHDIS(Dpa= 0) = -31.3 + 0.55 D0(X-H)
20
[N
HN
[C
lH ]
Cl
]
30
-
-
[O
[O
HO
HO
]
]
[F
HF
]


[B
rH
Br
]
-1
(a)
40
10
-
- -
0
(kcal mol-1; r =0.900, n =8)
80
90
100
110
120
130
120
80
2.5

showing, for the first time in the history of the H-bond, that
[
[O OH
HO O]
]
3.5
4.0
[F
HF
]
cP(X)
-1
(c)

40

30
20
[S
HS
]
[B
rH
Br
] [N
H
[N
[C N]
HN
lH
]
Cl
]
r =0.907, n =8),
EHB, MAX(X···X) (kcal mol)
(kcal
-
3.0
50
mol-1;
-
-
-
-
-
[O
[O
HO
HO
]
]
we obtain the final equation
-
[B
[C
[
rH
lH
Br [N NHN
Cl
] HN ]
]
]
[S
HS
]
100
90

-
110
(kcal mol-1; r =0.956, n =8),
EHB,MAX  DHDIS(Dpa= 0) = -44.8 + 21.6 cP(X)
-
-1
D0(X-H) (kcal mol )
130
[F
HF
]
140
D0(X-H) = -18.2 + 37.4 cP(X)
140
-1
D0(X-H) (kcal mol )
which shows that maximum H-bond energies are proportional to one half of the X-H bonddissociation 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.
(b)
Now, since D0(X-H) and the Pauling’s electronegativity cP(X) are linearly
related
-
[S
H
[N S]
HN
]
The following regression equation is obtained
EHB, MAX(X···X) (kcal mol)
1.2 The Importance of Electronegativity
50
-
-
-
10
0
the maximum energy achievable for any given X···H···X bond
is a linear function of c(X), the electronegativity of X.
2.5
3.0
3.5
cP(X)
4.0
Case study 1. Spa variable for Dpa= 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,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.
EHB = EHB,MAX exp[-k (d’D···A- d’D···A,min)]
4.5
4.0
3.5
EHB
3.0
F-H· · ·F
w
2.5
mw
m
dD...A (Å)
ms
s
2.0
EC(F,F)
40
Cl-H· · ·Cl
w
mw
m
ms
ms
s
30
w
mw
m
s
Br-H· · ·Br
(+)CAHB
EC(Cl,Cl)
(-)CAHB
EC(Br,Br)
(±)CAHB
20
OHB
10
d’D···A
0
O-H· · ·O
EHB
w
N-H· · ·O/O-H· · ·N
30
mw
w
N-H· · ·N
mw
w
mw
m
m
m
ms
ms
s
s
ms
s
EC(S,S)
S-H· · ·S
20
w
m
ms
EC(O,O)
EC(N,O)
EC(N,N)
s
10
d’D···A
0
4.5
4.0
3.5
3.0
2.5
dD...A (Å)
2.0
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)
EHB = 32.0 exp[-5.1 (d’D···A- 2.360)] (red figures set for the O–H···O bond)
4.5
4.0
3.5
EHB (kcal mol-1)
O-H· · ·O
w
N-H· · ·O/O-H· · ·N
30
w
ms
mw
mw
20
m
mw
w
N-H· · ·N
w
3.0
s
m
m
m
ms
ms
2.5
d'D···A (Å)
ms
s
s
s
2.0
(+)CAHB
(-)CAHB
S-H· · ·S
(±)CAHB
10
OHB
0
4.5
4.0
3.5
3.0
2.5
d'D···A (Å) 2.0
Let’s take the homonuclear O–H···O bond as an example:
The red horizontal line indicates the full range of O···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 of 2.36 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
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 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  D···H···A  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).
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
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
R–D–H····:A–R’  R–1/2-D···H+···A1/2––R’  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 by two H-bond donors (two acids)
R1–D1–H····:D2–-R2  [R1-D1···H···D2-R2]-  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 by two H-bond acceptors (two bases)
R1-+A1-H····:A2-R2  [R1-A1···H···A2-R2]+  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 (-)CAHBs and (+)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
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.
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.
Practical Use of the pKa Slide Rule: The Water-Water Dimer
-15 -13 -11 -9 -7 -5 -3 -1 0 1
MEDIUM
H
A+ D
MEDIUM
STRONG
H
STRONG
3
5
7
ANILINES
DIAMINES (2nd pKa)
1,2-PHOSPHINES
3-PHOSPHINES
SE-OXIDES
N-OXIDES
BARBITURIC ACID
D
MEDIUM
STRONG
MEDIUM
H-Bond Strength
H
MEDIUM
WEAK
G &G
THE pKa SLIDE RULE
DpKa
A
WEAK
49
45
43
39
41
37
BETTER BASE
9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
A
35
49
BETTER ACCEPTOR
HB ACCEPTORS (:A)
47
pKBH+
PROTON SPONGES
AMIDINES
31
27
25
23
21
19
NH3
H-H
17
AMINES
15
AZINES
13
11
NH39
7
5
3
1
HO-
H 2O
-1
AZOLES
33
45
43
41
37
39
35
33
29
25
27
21
31
AMINES
ANILINES
ALCOHOLS
H2O
HS-3
BETTER ACID
1,2-NITROANIL
H2BO3-
HPO42-5
-7
3
H2O2
HCN H3BO3
HCO - H4SiO4
-9
-11
-13
HBF4
H3PO4 HSO4HF
HNO2
HSCN
HNO3
H2SO4
HClO4
HI
HBr
HCl
HNNN
H2CO3 NH2OH
H2S H2PO4-
OXIMES
CARB ACIDS
PHENOLS
HAL-PHEN
NITROPHEN HAL-ALCOHOLS
SULFIDES
HAL-ANILINES
3-NITROANIL
AZO-COMPS
1,2-NITROANIL
ALDEHYDES
AMIDES
KETONES
S-OXIDES
NITRO
ALCOHOLS
ETHERS
COMPS
ACIDS
UREA
ESTERS
Ph3P=O
-D
HB DONORS (D-H)
47
pKAH
TRINITROANIL
NITRILES
BETTER DONOR
PYRROLES
INDOLES
29
ENOLS
TRINITRO PHENOLS
SULPHONIC ACIDS
23
AMIDES
THIOLES
HAL-CARB ACIDS
CF3-SO3H
19
15
17
13
9
11
7
5
3
1
-1
-3
-5
-9
-7
-11
-13
-15
 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
(±)CAHB
20
OHB
EHB = EHB,MAX exp[-k (d’D···A- d’D···A,min)]
10
0
O-H· · ·O
EHB
w
N-H· · ·O/O-H· · ·N
30
mw
w
N-H· · ·N
mw
w
mw
m
m
m
ms
ms
s
EC(N,O)
s
ms
EC(N,N)
s
EC(S,S)
S-H· · ·S
20
w
m
ms
EC(O,O)
s
10
d’D···A
0
4.5
4.0
3.5
3.0
Diagnosis for the Water Dimer:
d’O···O ≈ 2.70 Å
EHB ≈ 5 kcal mol-1
2.5
dD...A (Å)
2.0
-15 -13 -11 -9 -7 -5 -3 -1 0 1
-D
MEDIUM
H
A+ D
MEDIUM
STRONG
H
STRONG
3
5
G &G
THE pKa SLIDE RULE
9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
A
D
MEDIUM
STRONG
MEDIUM
H-Bond Strength
DpKa= 2.1
H-Bond Strength = STRONG
H
MEDIUM
WEAK
DpKa
A
WEAK
49
HB ACCEPTORS (:A)
47
pKBH+
BETTER BASE
43
41
39
37
35
H-H
33
NH3
31
27
25
29
BETTER ACCEPTOR
49
45
HB DONORS (D-H)
47
pKAH
43
41
37
39
35
33
31
29
27
23
21
23
19
PROTON SPONGES
AMIDINES
ANILINES
DIAMINES (2nd pKa)
1,2-PHOSPHINES
3-PHOSPHINES
SE-OXIDES
N-OXIDES
BARBITURIC ACID
7
17
15
AMINES
AMINES
ANILINES
HO-
H 2O
H2BO3HS-
AZINES
BETTER ACID
1,2-NITROANIL
ALCOHOLS
13
11
AZOLES
NH39
HCN H3BO3
HCO3- H4SiO4
H2O2
HPO427
5
3
1
HBF4
H3PO4 HSO4HF
HNO2
-1
H2O
HSCN
-3
-5
-7
HI
HBr
HCl
-9
-11
-13
HNO3
H2SO4
HClO4
CF3-SO3H
HNNN
H2CO3 NH2OH
H2S H2PO4-
OXIMES
CARB ACIDS
PHENOLS
HAL-PHEN
NITROPHEN HAL-ALCOHOLS
SULFIDES
HAL-ANILINES
3-NITROANIL
AZO-COMPS
1,2-NITROANIL
ALDEHYDES
AMIDES
KETONES
S-OXIDES
NITRO
ALCOHOLS
ETHERS
COMPS
ACIDS
UREA
ESTERS
Ph3P=O
BETTER DONOR
PYRROLES
INDOLES
45
ENOLS
TRINITROANIL
NITRILES
25
AMIDES
THIOLES
HAL-CARB ACIDS
TRINITRO PHENOLS
SULPHONIC ACIDS
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-9
-7
-11
-13
-15
Practical Use of the pKa Slide Rule: Urea-Phosphoric Acid
(±)CAHB
20
OHB
EHB = EHB,MAX exp[-k (d’D···A- d’D···A,min)]
10
0
O-H· · ·O
EHB
w
N-H· · ·O/O-H· · ·N
30
mw
w
N-H· · ·N
mw
w
mw
m
m
m
ms
ms
s
EC(N,O)
s
ms
EC(N,N)
s
EC(S,S)
S-H· · ·S
20
w
m
ms
EC(O,O)
s
10
d’D···A
0
4.5
4.0
CRBAMP01:
N-100K
d’O···O ≈ 2.409 Å
3.5
3.0
2.5
dD...A (Å)
2.0
Diagnosis for Urea-Phosphoric Acid:
d’O···O ≈ 2.42 Å
EHB ≈ 22 kcal mol-1
A Gallery of the Most Famous Strong H-bonds
12.80
21.39
22.35
23.21
23.69
12.89
14.99
15.30
24.50
(-)CAHB
32.42
21.83
22.39
23.09
22.17
22.54
22.17
18.29
20.56
20.88
24.30
22.17
9.00
12.78
13.87
13.31
13.52
22.17
14.52
23.81
(±)CAHB
21.39
(+)CAHB
24.80 26.23
10.87
P. Gilli et al., Acc. Chem. Res. (2009); EHB values (kcal mol-1) calculated by the exponential equation
Systematic Applications of the pKa-Equalization Methods:
1. N-H···O/O-H···N Bonds are DpKa-Modulated over the Full DpKa Range
When evaluated from the pKa slide rule, the total DpKa range is enormous: –30 DpKa  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).
1. N-H···O/O-H···N Bonds are DpKa-Modulated over the Full DpKa Range
(Continued)
Increasing Acidity of the Protonated A-H+ Acceptor
Increasing Basicity of the :A Acceptor
DpKa large
& positive
HBs weak
& neutral
Increasing Acidity of the D-H Donor
HB-strengths
 color code
HBs weak
& charged
DpKa large
& negative
From: P. Gilli et al., Acc. Chem. Res. 42: 33-44 (2009)
1. N-H···O/O-H···N Bonds are DpKa-Modulated over the Full DpKa 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
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.
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, DegaSzafran, 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.
pKa=
-0.7
O
H
O
pKa= O
-12
O
N
O
Cl
O
O
N
N
O
pKa=
0.35 H
pKa=
-12
pKa=
4.74
H
O
O
Cl
N
O
pKa=
3.54 H
Cl
Cl
N
N
N
O
O
Dichloropicric acid
Cl
Cl
Cl
Cl
O
O
O
pKa=
-12
Picric acid
O
Cl
O
2,6-Dichloro4-nitrophenol
Pentachlorophenol
EHB versus d’D···A Scatterplot
in Nitro- and Halogeno-Phenol Complexes with N- and O-Bases
EHB = EHB,MAXexp[-k (d'O···O- d'O···O,min)]
(EHB,MAX= 32.0; k = 6.43(6); d'O···O,min= 2.360;
n = 38; r = 0.994)
25
Our Data:
Picric Acid OHO
Picric Acid OHN
Picric Acid OHO(nitro)
+
Picric Acid OHN (nitro)
CSD Data:
Picric Acid OHO
Picric Acid OHN
NO2-Phenols OHO
NO2-Phenols OHN
Cl2-Picric Acid OHO
Cl5-Phenol OHO
Cl5-Phenol OHN
Exponential fit on 38 points
Exponential fit on 70 points
EHB = EHB,MAXexp[-k (d'O···N- d'O···N,min)]
(EHB,MAX= 15.2; k = 5.53(6); d'O···N,min= 2.506;
n = 70; r = 0.997)
20
-1
EHB,O···X (kcal mol ); X= O, N
30
15
10
5
0
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
d'O···X = dO-H + dH-X (Å); X= O, N
 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 EHB versus d’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.
EHB versus DpKa Scatterplot
in Nitro- and Halogeno-Phenol Complexes with N- and O-Bases
EHB = EHB,MAXexp[-k (DpKa°-DpKa)]
(EHB,MAX= 24.0; k = 0.214(9); DpKa° = 3.0;
n = 95; r = 0.84)
Our Data:
Picric Acid OHO
Picric Acid OHN
Picric Acid OHO(nitro)
+
Picric Acid OHN (nitro)
CSD Data:
Picric Acid OHO
Picric Acid OHN
NO2-Phenols OHO
NO2-Phenols OHN
Cl2-Picric Acid OHO
Cl5-Phenol OHO
Cl5-Phenol OHN
Exponential fit on 95 points
20
15
-1
EHB,O···X (kcal mol ); X= O, N
25
10
5
0
-25
-20
-15
-10
-5
0
DpKa
5
 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.
d’D···A versus DpKa Scatterplot
in Nitro- and Halogeno-Phenol Complexes with N- and O-Bases
3.6
d'O···X = 2.53(1) - 0.037(1) DpKa
(n = 95; r = -0.952; P < 0.0001)
3.5
Our Data:
Picric Acid OHO
Picric Acid OHN
Picric Acid OHO(nitro)
+
Picric Acid OHN (nitro)
CSD Data:
Picric Acid OHO
Picric Acid OHN
NO2-Phenols OHO
NO2-Phenols OHN
Cl2-Picric Acid OHO
Cl5-Phenol OHO
Cl5-Phenol OHN
Linear fit on 95 points
95% Confidence limits
95% Prediction limits
d'O···X = dO-H + dH-X (Å); X=O, N
3.4
3.3
3.2
3.1
3.0
2.9
2.8
2.7
2.6
2.5
2.4
-25
-20
-15
-10
-5
0
DpKa
5
 The shape of the d’D···A 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.
A 3-Dimensional DpKa / EHB / d’D···A Correlation
in Nitro- and Halogeno-Phenol Complexes with N- and O-Bases
END of LECTURE