Advances in
Physical Organic Chemistry
Volume 44

Editor
JOHN P. RICHARD
Department of Chemistry
University at Buffalo, SUNY
Buffalo, NY, USA

Amsterdam – Boston – Heidelberg – London – New York – Oxford
Paris – San Diego – San Francisco – Singapore – Sydney – Tokyo
Academic Press is an imprint of Elsevier


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Contributors to Volume 44
Claude F. Bernasconi Department of Chemistry and Biochemistry,
University of California, Santa Cruz, CA 95064, USA
W.W. Cleland Department of Biochemistry and Institute for Enzyme
Research, University of Wisconsin-Madison, Madison WI 53726, USA
Ronald Kluger Davenport Chemistry Laboratories, Department of
Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
Scott O.C. Mundle Davenport Chemistry Laboratories, Department of
Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
Rory More O’Ferrall School of Chemistry and Chemical Biology,
University College Dublin, Belfield, Dublin 4, Ireland
Charles L. Perrin Department of Chemistry & Biochemistry, University of
California—San Diego, La Jolla, CA 92093-0358, USA
Jakob Wirz Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland

Hiroshi Yamataka Department of Chemistry, College of Science and
Research Institute for Future Molecules, Rikkyo University, Tokyo, Japan

xi


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The low-barrier hydrogen bond in enzymic
catalysis
W.W. CLELAND
Department of Biochemistry and Institute for Enzyme Research, University
of Wisconsin-Madison, Madison, WI 53726, USA
1 Introduction 1
2 Properties of hydrogen bonds 1
3 Role of low-barrier hydrogen bonds in enzymatic reactions 3
Enolization reactions 3
Facilitated tetrahedral intermediate formation 6
Facilitated proton ionization 10
Aspartic proteases 12
Miscellaneous enzymes 13
Acid–Base catalysis 14
4 Conclusion 15
References 15

1

Introduction

The term ‘‘low-barrier hydrogen bond’’ was introduced by me in 1992

to describe hydrogen bonds between groups of equal pK that showed low
deuterium fractionation factors (as low as 0.3).1 It was not until an Enzyme
Mechanisms conference in Key Largo, however, that a number of us finally
realized how such bonds can help catalyze enzymic reactions and papers
describing this appeared in 1993 and 1994.2–5 Since then such bonds have
been shown to play a role in many enzymic reactions and a Google search
under ‘‘low-barrier hydrogen bond’’ turns up over 5000 hits. In this review I
shall describe the properties of low-barrier hydrogen bonds and then give a
number of examples. I have not tried to cover the entire literature and
apologize to those whose works are not mentioned.

2

Properties of hydrogen bonds

Hydrogen bonds come in a continuum of bond lengths and strengths.
Those in water which hold it together as a liquid are $2.8 A˚ between
oxygens and are weak (only a few kcal molÀ1). Since the pK of water as
an acid is above 15 and its pK as a base is less than –1, the pK’s of the two
1
ADVANCES IN PHYSICAL ORGANIC CHEMISTRY
VOLUME 44 ISSN: 0065-3160 DOI: 10.1016/S0065-3160(08)44001-7

Ó 2010 Elsevier Ltd.
All rights reserved


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2


W.W. CLELAND

oxygens in the hydrogen bond are drastically different and the hydrogen is
covalently bound to one oxygen with a bond distance of 1 A˚ and weakly
bonded electrostatically to the other oxygen. When the pK’s of the two
groups are the same, as in a hydrogen bond between formic acid and
formate ion, the bond is shorter (2.5–2.6 A˚) and the zero point energy
level of the hydrogen is at or above the barrier (thus ‘‘low-barrier hydrogen bond,’’ Fig. 1).6–8 Neutron diffraction of crystals containing such
bonds show a diffuse distribution centered between the two heavy
atoms.9 In certain cases where the bond is especially short, there is no
barrier as in the F–H–FÀ or HO–H–OHÀ ions which are only 2.3 A˚
long.10,11 Low-barrier hydrogen bonds are quite strong (as much as 27 kcal
molÀ1 in the gas phase and perhaps 12 in aqueous solution7), but in a
medium with a dielectric constant of $7 (similar to what occurs in an
enzyme active site) the strength decreases by $1 kcal molÀ1 per pH unit
mismatch in the pK’s of the groups involved.12 Thus there is a continuum
between the very strong ones with matched pK’s and the weak ones with
very different pK’s and the distances similarly differ as well. Low-barrier
hydrogen bonds have considerable covalent character,6,13 which decreases
as the bonds weaken and lengthen, so that the weak ones are only
electrostatic in nature.
As noted in 1992, low-barrier hydrogen bonds show low fractionation
factors, with up to threefold discrimination against deuterium. They show
downfield chemical shifts in proton nuclear magnetic resonance (NMR) of
18–20 ppm. At first it was thought that they only occur in the gas phase or
organic solvents, but it is now clear that they can occur in solutions containing
a high mole fraction of water, even at room temperature.14,15 What limits their
determination in aqueous solution is rapid exchange with solvent protons.
Hydrogen bonds can occur between two oxygens, two nitrogens, or one

of each. We will show examples of O–O and O–N bonds in the discussion
below.

(a)

O
O

(b)

H
H

O
O

O

(c)

H

O

O

H

O


Fig. 1 Energy diagrams for hydrogen bonds between groups of equal pK. (a) Weak
hydrogen bond; O–O distance 2.8 A˚. (b) Low-barrier hydrogen bond (2.55 A˚); the
hydrogen diffusely distributed. (c) Single-well hydrogen bond (2.29 A˚). Horizontal
lines are zero point energy levels for hydrogen (upper) and deuterium (lower).


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THE LOW-BARRIER HYDROGEN BOND IN ENZYMIC CATALYSIS

3

3

Role of low-barrier hydrogen bonds in enzymatic reactions

ENOLIZATION REACTIONS

The first examples of enzymatic reactions where low-barrier hydrogen bonds
played a role involved enolization of the substrate to change the pK of a key
group in the reaction. Mandelate racemase enolizes R or S mandelate to
convert the carboxyl group into an aci-carboxylate which can be protonated
on opposite sides to give the R or S forms. In the ground state, one oxygen of
the carboxyl group of mandelate is coordinated to Mg2ỵ and the other oxygen
is hydrogen bonded to Glu317 which is protonated.16 The pK of a CTO group
is low, so this is a weak hydrogen bond. In the aci-carboxylate intermediate,
however, the pK of its oxygen will be similar to that of Glu317 and the
hydrogen bond becomes a low-barrier one (Fig. 2). The energy liberated by
formation of the strong hydrogen bond lowers the activation for formation of
the intermediate. The 105 reduction in kcat for the E317Q mutant supports

this model.17
A similar situation occurs with triose-P isomerase, where Glu165 abstracts
a proton from either glyceraldehyde-3-P or dihydroxyacetone-P to give
an enediolate intermediate. The carbonyl group of the substrate is hydrogen
bonded to a neutral imidazole in the active site; this will be a weak hydrogen
bond because of the huge mismatch in pK’s.18 The pK of both the imidazole
and the enediol intermediate, however will be $11, and thus this hydrogen
bond becomes a low-barrier one in the intermediate Fig. 3). An isoenergetic
shift of the imidazole from one OH to the other shifts the strong hydrogen
bond to the oxygen destined to become a carbonyl group when the
intermediate is protonated by Glu165 to complete the reaction.
Ketosteroid isomerase is another enzyme in which enolization of the
substrate changes the pK of a key atom so that a low-barrier hydrogen bond
forms and helps stabilize the intermediate. Asp38 is the general base that
removes a proton from the substrate, and Tyr14 is hydrogen bonded to the
carbonyl oxygen of the substrate. The pK’s of a ketone and of tyrosine are

Mg

Mg

HO

HO
O

C
H

O


C

C
O

Lys166
(bases)
His297

C

H Glu

O

H

Glu

H-base

Fig. 2 Mechanism of mandelate racemase.16,17 Lys166 and His297 are the two general
bases and are on opposite sides of mandelate.


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W.W. CLELAND
H
Glu– HC

H
OH

C

OH

C

O

GluH
C

O

HN

N

H

CH2OPO32–

CH2OPO32–


H

H

C

O

HN

N

C

O

C

OH

H

N

N

N

N


GluH
Glu– HC

OH

CH2OPO32–

CH2OPO32–

Fig. 3 Mechanism of triose-P isomerase.4 Note the isoenergetic shift of the histidine
between the two OH groups of the enediolate intermediate; a low-barrier hydrogen
bond is present in both structures.

drastically different, but in the dienolate intermediate, the pK’s become
more similar. An analog aromatic in the A ring and containing a phenolic
hydroxyl in place of the ketone bound at least 1000-fold tighter to the D38N
mutant than to wild-type isomerase.19 The neutral Asn38 mimics the protonated state of Asp38 after the formation of the intermediate dienolate. In the
inhibitor complex proton NMR peaks were at 18.15 and 11.6, with the proton
at 18.15 having a deuterium fractionation factor of 0.34 and the hydrogen
bond having a strength of 7.1 kcal molÀ1 more than one between inhibitor and
water. This increase in hydrogen bond strength corresponds to over 5 orders
of magnitude rate acceleration and matches the decrease in rate of 4.7 orders of
magnitude in the Y14F mutant.
Subsequent work has shown that Asp99 is involved in the hydrogen bond
network in this enzyme and the 18.15 ppm NMR peak is from a hydrogen
bond between it and Tyr14.20 The 11.6 ppm peak comes from the hydrogen
bond between the intermediate and Tyr14. Despite this complexity, it is
still true that formation of a strong hydrogen bond in the presence of the
intermediate decreases the activation energy of the reaction and thus provides
catalysis.

Aconitase contains a 4Fe–4S center with citrate or isocitrate binding with
one of their carboxyl groups and the OH group coordinated to the Fe at one
corner of the Fe–S cluster.21,22 A water molecule is also coordinated to this


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THE LOW-BARRIER HYDROGEN BOND IN ENZYMIC CATALYSIS

5

Fe and is hydrogen bonded to a free carboxyl group. The general base for the
elimination reaction is Ser642, which donated its proton to the Fe-bound
hydroxide when the substrate bound. Proton removal by Ser642 produces an
aci-carboxylate from the carboxyl next to the carbon from which the proton
was removed, and the pK of the aci-carboxylate now is a close match to the
pK of the Fe-bound water to which it is hydrogen bonded. This hydrogen
bond thus becomes a low-barrier one, its formation providing part of the
energy needed to form the aci-carboxylate (Fig. 4). His101 then protonates
the Fe-coordinated OH of the substrate to allow it to be eliminated to give
cis-aconitate.
In the E-isocitrate X-ray structure the hydrogen bond between the Fe-bound
water and the carboxyl of isocitrate is 2.7 A˚ long, while in a similar structure
with the nitro analog of isocitrate bound as an aci-nitronate the distance is
2.5 A˚.21
Citrate synthase catalyzes the enolization of acetyl-CoA and attack of
the enolate on oxaloacetate to form citryl-CoA, which is then hydrolyzed.
Asp375 takes the proton from the methyl group of acetyl-CoA and neutral
His274 hydrogen bonds to the carbonyl oxygen to stabilize the enolate.23
X-ray structures of carboxyl or amide analogs of acetyl-CoA showed

2.4–2.5 A˚ hydrogen bonds between the carboxyl or amide group of the inhibitor (replacing the methyl of acetyl-CoA) and Asp375.24 The Ki of the amide
inhibitor was pH independent, while that of the carboxylate decreased as the
pH decreased, showing that the protonated form was the inhibitor. The
carboxyl inhibitor binds 4 orders of magnitude tighter than acetyl-CoA and
thus the low-barrier hydrogen bond (chemical shift 20 ppm25) contributes at
least this much to binding. During the catalytic reaction, the low-barrier
hydrogen bond should be between His274 and the enolate oxygen, since their
pK’s will be similar, and the energy from formation of the stronger hydrogen
bond will help catalyze the enolization (Fig. 5).
Vitamin K-dependent carboxylase uses vitamin K epoxidation to drive the
carboxylation of glutamate groups in Gla domains. It is thought that reaction
of oxygen with reduced vitamin K produces a strongly basic form of an

H

H
OH
Fe

O

Fe

O

O HO
C

O


C
H

H His
C

C
CH2

H
– –
O Ser

O HO

O

C
COO–

O

C

H
H

H His
C


OH
Fe

O
C
CH2

H
HO–Ser

O

O HOH

O–

C
COO–

O

C

His
C

C
CH2

H


O

COO–

HO–Ser

Fig. 4 Mechanism of aconitase.4 The aci-carboxylate intermediate shares a
low-barrier hydrogen bond with the Fe–OH group.


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6

W.W. CLELAND
COO–

O

HN

N

COO–

O

C


C SCoA

H

N

N

Arg

Arg
O

C

CH3

O

C SCoA

CH2

His

His
CH2

CH2


Asp–

COO–

AspH

COO–

COO–

O

HN

N

COO–

O

C

C SCoA

HN

N

Arg


Arg
HO

C

CH2

HO

C SCoA

CH2

His

His
CH2

Asp–

COO–

COO–

O

H

Arg


N

N

CH2

O

H

COO–

H

Asp

COO–

O

HN

C

C

N

Arg
HO


C

CH2

HO

C SCoA

His

CH2

His
CH2

O
–

COO

H Asp

H

CH2
COO

H + HSCoA


O
–

Asp

–

Fig. 5 Putative mechanism of citrate synthase.4 A low-barrier hydrogen bond helps to
stabilize the enol and tetrahedral intermediates.

epoxide that removes a proton from a glutamate residue to give a carbanion
intermediate that reacts with CO2. It was recently found that a H160A
mutant carried out epoxidation readily, but carboxylation very poorly.26 It
was postulated that His160 forms a hydrogen bond to one oxygen of the
carboxyl group of glutamate. This will be a weak hydrogen bond before
enolization, but proton removal will give an aci-carboxylate whose pK is a
close match to that of neutral histidine. Thus the authors proposed that a
low-barrier hydrogen bond between aci-carboxylate and His160 helped to
stabilize the intermediate. As yet there is no structural evidence in support of
this attractive hypothesis.

FACILITATED TETRAHEDRAL INTERMEDIATE FORMATION

A low-barrier hydrogen bond forms between Asp102 and His57 in the
tetrahedral intermediate of the reaction catalyzed by chymotrypsin and similar
serine proteases. In the free enzyme the pK of Asp102 and the neutral form of
His57 are quite different, but when the Ser195 proton is transferred to His57
during formation of the tetrahedral intermediate, the pK’s of Asp102 and
protonated His57 now become matched and the hydrogen bond between



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THE LOW-BARRIER HYDROGEN BOND IN ENZYMIC CATALYSIS

7

them becomes a low-barrier one, thus providing the energy for formation of
the unstable intermediate (Fig. 6).5 Transfer of the proton from His57 to the
leaving amino group gives an acyl enzyme and dissipates the strength of the
His57 O
Ser195

:N

OH

N H

C

Asp102

C

Asp102

O

O

C
Peptidyl

NHR

O
C
Peptidyl
Ser195

His57 O

NHR
:N

OH

N H

O

O–

Peptidyl
C

His57 O

NHR


y–

Ser195

O

HN

y+

N

H

C

Asp102

O

H2NR

O

Peptidyl

His57 O

C


C
Ser195

O

:N

N H

Asp102

O

Fig. 6 Mechanism of chymotrypsin.5 A low-barrier hydrogen bond between Asp102
and His57 helps stabilize the tetrahedral intermediate.


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8

W.W. CLELAND

low-barrier hydrogen bond. Clear evidence for this mechanism is provided
by observation of tetrahedral adducts of trifluoromethyl ketone inhibitors
with the enzyme. In these complexes the proton chemical shift of the proton
in the Asp102–His57 hydrogen bond is 18–19 ppm and the fractionation
factor is 0.3–0.4. The exchange rate of the proton with the solvent ranges
from 282 sÀ1 for N–AcF–CF3 with a Ki of 26 mM to 12.4 sÀ1 for N–AcLF–CF3
with a Ki of 1.8 mM. The pK of His57 in these complexes is 10.7 or 12.1.

The pK of 12.1 is 5 pH units higher than that in free enzyme, corresponding to
5 orders of magnitude rate acceleration.27,28
This situation was mimicked by observing complexes of N-alkylimidazoles
with carboxylic acids in chloroform.29 As the pK of the acid increased, the
chemical shift of the proton in the hydrogen bond moved downfield to 18 ppm
and then moved back upfield. With 2,2-dichloropropionate the chemical
shift of 18 ppm did not change with dilution, suggesting a strong hydrogen
bond between the two molecules. The chemical shifts of complexes with
more upfield protons moved further upfield on dilution, showing that
they were weaker. Calorimetric measurements of complexes between
2,2-dichloropropionate and N-methyl or N-t-butylimidazole gave values of
12 or 15 kcal molÀ1 for the enthalpy of formation.30 The IR spectrum of a
complex with 2,2-dichloropropionate showed two peaks for the CTO stretch
at 1700 cmÀ1 for the low-barrier hydrogen bond ($2/3 of the complex) and
1647 cmÀ1 for the edge-on ion pair where the carboxyl group is perpendicular
to the ring of the imidazole and both oxygens are in contact with the positively
charged nitrogens ($1/3 of the complex). The NMR shift of 18 ppm is an
average for the two species, which are in rapid equilibrium on the NMR
timescale.
An 0.78 A˚ structure of subtilisin resolved the proton between His64
and Asp32 of the catalytic triad.31 The distance of the hydrogen bond was
2.62 A˚ with the proton 1.2 A˚ from His64 and 1.5 A˚ from Asp32. The authors
felt that this was not a low-barrier hydrogen bond because His64 was not
protonated, but the short distance suggests that when His64 does become
protonated during formation of the tetrahedral intermediate, it will become
a low-barrier one.
For the reaction catalyzed by cytidine deaminase, an analog of cytidine
where the 3–4 bond is a single one and there is a hydroxy group at C4
(zebularine 3,4-hydrate) is a competitive inhibitor with a Ki of 10À12 M.32 An
X-ray structure of this inhibitor bound to the enzyme shows a 2.45 A˚ hydrogen

bond between the OH group at C4 and the carboxylate of Glu104.33 The OH
group is also coordinated to a Zn2ỵ ion and the other oxygen of Glu104 is
hydrogen bonded to N3 (2.74 A˚). This structure corresponds to the putative
tetrahedral intermediate formed by attack of the Zn-bound hydroxyl group on
C4 of the pyrimidine ring, but with the amino group at C4 replaced with
hydrogen (Fig. 7). It appears that the formation of a low-barrier hydrogen
bond between the OH group and Glu104 may provide some of the energy


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THE LOW-BARRIER HYDROGEN BOND IN ENZYMIC CATALYSIS

9

His102
Cys132

S
Zn

S

C
C

Glu104

2.49Å
O H O

H

C

Cys129

HN

O
HN
O

NH

N

Ala103

Ribose

Fig. 7 Structure of cytidine deaminase with zebularine 3,4-hydrate bound.33 The lowbarrier hydrogen bond between Glu104 and the Zn–OH would help stabilize the
tetrahedral intermediate, which would have an NH2 in place of the H at C4 of the
ring in this structure.

needed to form the tetrahedral intermediate. Transfer of the proton in this
bond to the amino group then permits it to leave as ammonia to complete the
reaction. However, the proton NMR spectrum of the bound inhibitor did not
show any downfield peaks that could be assigned to a low-barrier hydrogen
bond, so its importance in the reaction is uncertain.
Thermolysin and carboxypeptidase use Zn2ỵ to polarize the carbonyl group

of the amide substrate to permit attack by Zn-bound water. A glutamate
residue (143 in thermolysin and 270 in carboxypeptidase) acts as a general
base and is hydrogen bonded to the Zn-bound water. A proton is transferred
to the leaving nitrogen, which permits the tetrahedral intermediate that is
bidentately coordinated to Zn to decompose to the final products of the
reaction (Fig. 8). The tetrahedral intermediate has been mimicked by several
phosphonates with Ki values as low as 10 fM. X-ray structures show these
inhibitors as bidentate ligands of Zn and the hydrogen bond between the
catalytic glutamate and one Zn-coordinated oxygen of the phosphono group
is 2.3–2.5 A˚ in the three structures of each of the two enzymes.34–37 These short

R–NH

Glu

H

R–NH

R
C

H
O

O
Zn

Glu


H

R

R–NH

C

H

O

O
Zn

Glu

H

R

R–NH

C

H
O

O
Zn


Glu

H

R
C

H

O

O
Zn

Fig. 8 Mechanism of thermolysin and carboxypeptidase based on X-ray structures of
enzymes with bound phosphonate inhibitors.34–37


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10

W.W. CLELAND
18.00 ppm
12.67 ppm
(normal H-bond) (strong H-bond)
His48

Asp99


CH2–(CH2)5–CH3
O

O–

H

N

N

H

Oδ–

P

Oδ–
O

O
H3C–(CH2)7 –S–CH2

C
H

H2C

O


P

O

+

(CH2)2 –NH3

O–

Fig. 9 Structure of phospholipase A2 with bound phosphonate inhibitor mimicking
the tetrahedral intermediate.38

distances suggest that this hydrogen bond in the tetrahedral intermediate is a
low-barrier one, with the energy released by its formation helping to form the
high-energy intermediate.
Phospholipase A2 catalyzes the hydrolysis of phospholipids at the sn-2 bond,
using a water molecule coordinated to Ca2ỵ. Enzymes from bovine pancreas
and bee venom are similar in many respects and both contain an aspartate
and histidine as catalytic groups. In the presence of phosphonate inhibitors
that mimic a tetrahedral intermediate, a low-barrier hydrogen bond exists
between the histidine and a phosphonate oxygen, while the hydrogen bond
between the histidine and aspartate is a normal one (Fig. 9).38 The proton
NMR chemical shifts for the protons in the low-barrier hydrogen bond is
$18 ppm, while the other proton has a chemical shift of $13 ppm. The lowfield proton has a fractionation factor of 0.6 and the pK of the histidine is
shifted from 5.7 in free enzyme to 9 in the presence of the inhibitor. This
suggests a minimum of 4.5 kcal molÀ1 extra energy made available for catalysis
by the low-barrier hydrogen (the actual value is probably higher, as the
inhibitor dissociates when the histidine is deprotonated).


FACILITATED PROTON IONIZATION

In the liver alcohol dehydrogenase reaction the alcohol substrate is bound to a
Zn2ỵ ion in the active site. The proton of the OH group is transferred via a
hydrogen bond network involving Ser48 and the ribose 20 -OH of NAD to
His51. Hydride transfer from the alkoxide intermediate then completes the
reaction. In a structure with NAD and pentafluorobenzyl alcohol bound, the
distance between the oxygens of the alcohol and Ser48 is 2.5 A˚.39 In D2O
solvent isotope effects on single turnover reactions of benzyl alcohol with


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THE LOW-BARRIER HYDROGEN BOND IN ENZYMIC CATALYSIS

11

E-NAD, the fractionation factor of the proton between the alcohol and Ser48
was 0.37 and that in the transition state was 0.73, partway to $1.0, the value
expected for the weak hydrogen bond between Ser48 and the aldehyde product.40 It thus appears that in the alkoxide intermediate the hydrogen bond
between the alcohol substrate and Ser48 is a low-barrier one, with the energy
released by its formation driving the proton movement to His51, which would
otherwise not be energetically favorable (Fig. 10).
UDP-galactose 4-epimerase contains bound NAD and catalyzes the interconversion of UDP-glucose and UDP-galactose via a 40 -keto intermediate. Two
residues, Ser132 and Tyr157 are in close proximity of the 40 -OH of the substrate,
with Ser132 only 2.5 A˚ from the 40 -OH. It was postulated that Tyr147 is the
general base for proton removal from the 40 -OH during hydride transfer to give
the 40 -keto intermediate, but that a low-barrier hydrogen bond between Ser132
and the 40 -OH provided the energy to help drive the process.41 This situation is

reminiscent of that with liver alcohol dehydrogenase discussed above.
Yeast pyrophosphatase uses a water molecule bound between two Mg2ỵ
ions as the nucleophile to attack bound Mg-pyrophosphate. Asp117 acts as a
general base to deprotonate this bound water, whose pK is 5.85.42 It was
suggested on the basis of X-ray structures and the similar pK’s that the
hydrogen bond between Asp117 and the nucleophilic water was a low-barrier
one.43 Coordination to both Mg2ỵ ions as well as formation of a low-barrier
hydrogen bond should certainly be sufficient to lower the pK of the bound
water to the observed value.
Pyruvate decarboxylase binds thiamine diphosphate as its cofactor, and the
pK of the pyrimidine ring of the cofactor is 5.0. N10 of the ring can form a
hydrogen bond to Glu50 when the ring is in the 10 ,40 -imino tautomer and it
has been suggested that a low-barrier hydrogen bond forms between N10 and
Glu50 in order to enhance the proportion of imino tautomer, with the N40 NH
group then removing the proton to give the active ylide form of the cofactor
(Fig. 11).44

Zn
O
H

C

S48
H

Zn
δ

O


H NAD

H

O

H

C

H

S48

Zn

O

O
δ

NAD

H

C

R


R

R

ΦR = 0.37

ΦT = 0.73

ΦP = 1.0

S48
H

O
NADH

Fig. 10 Changes in the hydrogen bond between Zn–OH and Ser48 during hydride
transfer to NAD in the liver alcohol reaction.40 The È values are deuterium
fractionation factors.


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12

W.W. CLELAND
O
Glu

C

O

CH2
N
N

N

NH2 H

S

OPP
ThDP

O
Glu

C
O

H

CH2
N
N

N

NH H


S

OPP
1′,4′-imino
tautomer
of ThDP

O
Glu

C
O

H

CH2
N
N

NH2

N
S

OPP
ThDP ylide

Substrate


Fig. 11 Possible formation of a low-barrier hydrogen bond between Glu50 and bound
thiamin-PP to enhance the proportion of ylide in the pyruvate decarboxylase reaction.44

ASPARTIC PROTEASES

Aspartic proteases have two aspartates hydrogen bonded to each other and
sharing a water molecule between their other oxygens. This water then
becomes the nucleophile for attack on the substrate. Ab initio calculations
on human immunodeficiency virus (HIV)-1 protease found that the most
stable form is one where there is a low-barrier hydrogen bond (2.5 Æ 0.1 A˚)
between the aspartates and a net negative charge to the cluster (Fig. 12).45
Northrop then formulated a mechanism for the protease in which the lowbarrier hydrogen bond becomes a normal one as protons shift during attack on
the substrate to form a tetrahedral intermediate.46 The central proton then


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THE LOW-BARRIER HYDROGEN BOND IN ENZYMIC CATALYSIS

13

O
H

H

O

O
C


C
Asp25

O

H

O

Asp25′

Fig. 12 Low-barrier hydrogen bond between aspartates of HIV protease to generate
nucleophilic water.45 The overall cluster has a negative charge.

shifts back to the other aspartate as the leaving group is protonated and the
tetrahedral intermediate falls apart. Product release, replacement with water,
and deprotonation then reform the low-barrier hydrogen bond and the enzyme
is cocked for the next catalytic cycle.
In contrast to this proposal, X-ray and neutron diffraction studies of complexes of aspartic proteases with bound inhibitors have found hydrogen bonds
other than that between the two aspartates to be short and likely low-barrier
ones. The 1.03 A˚ structure of a complex with a phenylnorstatine inhibitor
shows a 2.97 A˚ hydrogen bond between the aspartates with the proton visible
midway between the two oxygens.47 By contrast, the hydrogen bonds from
the other oxygens of the aspartates to a hydroxyl and ketone of the inhibitor
are 2.61 and 2.55 A˚. A 1.65 A˚ structure with the products bound showed
the hydrogen bond between the two aspartates to be 2.30 A˚ long, certainly a
low-barrier hydrogen bond.48 In a neutron diffraction structure of endothiapepsin with an inhibitor thought to mimic the tetrahedral intermediate, hydrogen bonds from the aspartates to the hydroxyl of the inhibitor were $2.6 A˚,
and a hydrogen bond was not seen between the aspartates.49 A neutron
diffraction structure of endothiapepsin with an inhibitor with a gem-diol in

the active site showed hydrogen bonds of 2.54 and 2.65 A˚ between the gem-diol
oxygens and oxygens of the aspartates, while the other aspartate oxygens
were 2.93 A˚ apart.50 A 1.6 A˚ X-ray structure of HIV-1 protease with bound
products shows 2.4 and 2.45 A˚ hydrogen bonds from the aspartates to the
carboxyl of one product, with the distance between the other oxygens of the
aspartate being 2.95 A˚.51 It is clear from these structures that a number of
possible hydrogen bond orientations are possible, depending on what is bound.
Whether Northrop’s mechanism is correct in all of its details is not yet clear, but
it appears that low-barrier hydrogen bonds do play a role in aspartic proteases.

MISCELLANEOUS ENZYMES

A low-field resonance at 19.1 ppm is seen in the proton NMR spectrum of
2-amino-3-ketobutryate-CoA ligase. The signal is present only when the cofactor pyridoxal-P is bound and it was assigned to the proton between the


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14

W.W. CLELAND

pyridinium nitrogen and a putative aspartate.52 The pK of this signal was 6,
which is consistent with a low-barrier hydrogen bond. Such a bond would in
this case stabilize and help bind the cofactor in the proper position.
A structure of the N-terminal half of hen ovotransferrin has a 2.3 A˚ distance
between the terminal nitrogen atoms of Lys209 and Lys301 which are in
separate domains.53 It was proposed that this was a low-barrier hydrogen
bond holding the two domains together and that when the transferrin entered
an acidic endosome, the protonation of this lysine pair would cause the lysines

to move apart, thus allowing release of the bound Fe3ỵ. This lysine pair would
thus be a pH-sensitive trigger for Fe3ỵ release.
A recent neutron crystallography study of photoactive yellow protein
discovered a low-barrier hydrogen bond between the phenolic oxygen of the
4-hydroxycinnamic acid chromophore and Glu46 in the ground state.54 The
deuterium atom in the structure was 1.37 A˚ from the phenolic oxygen and
1.21 A˚ from the oxygen of Glu46. The role of the low-barrier hydrogen bond is
postulated to be stabilization of the negative charge on the chromophore and
Glu46 system. Upon photoactivation the chromophore is isomerized and the
hydrogen bond is no longer a low-barrier one, with the proton transferred
to Glu46.
In H148D mutants of green fluorescent protein it appears that a low-barrier
hydrogen bond is present between Asp148 and the phenolic oxygen of the
chromophore (2.4 A˚ in a S65T/H148D mutant).55 Despite the change in
hydrogen bonding in the active site, the Asp148 mutants permit fluorescence
in S65T and E222Q mutants, which do not fluoresce if His148 is still present.
A recent sub-A˚ngstrom X-ray structure of a phosphate-binding protein
showed that there are 11 hydrogen bonds to the phosphate oxygens from
OH or NH groups, and the proton on one oxygen of the phosphate dianion
forms a 2.5 A˚ low-barrier hydrogen bond with an aspartate.56 Formation of
this strong bond ensures that even at pH 4.5 the protein binds phosphate as the
dianion.

ACID–BASE CATALYSIS

Low-barrier hydrogen bonds are likely to form during general acid and general
base catalysis. In the lactate dehydrogenase reaction, for example, the hydroxyl group of lactate is weakly hydrogen bonded to His195 before catalysis and
weakly hydrogen bonded to the carbonyl oxygen of pyruvate after reaction.
As the hydride ion is transferred from lactate to NAD the pK of the oxygen on
lactate changes from $14 in lactate to $–5 in pyruvate. At the point where

the pK of this oxygen is $6, the pK’s of it and His195 will be matched and
the hydrogen bond will become a low-barrier one. As the pK’s diverge the
bond will weaken and the proton will transfer to His195. The transition state
for the reaction should be close to the point where the pK’s match and thus


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THE LOW-BARRIER HYDROGEN BOND IN ENZYMIC CATALYSIS

15

the energy released by forming the low-barrier hydrogen bond will lower the
activation barrier for the reaction. General acid–base catalysis provides as
much as 5 orders of magnitude rate acceleration in enzymatic reactions,
which is consistent with the energy provided by forming a low-barrier
hydrogen bond in the transition state.57

4

Conclusion

It should be clear from this brief review that low-barrier hydrogen bonds play
an important role in many enzymatic reactions, in many cases contributing the
energy of their formation to provide catalysis. I have not reviewed the extensive computational literature on low-barrier hydrogen bonds, but an early
review will provide more information.10 Other short reviews on their role in
enzymatic reactions have been published.4,15,58,59 I have not included references to early critics of the role of low-barrier hydrogen bonds, as I think their
criticisms have been shown to be invalid. References to those articles are
available in the reviews noted above.


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Remington SJ. Curr Opin Struct Biol 1992;2:730–5.
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Gu Z, Drueckhammer DG, Kurz L, Liu K, Martin DP, McDermott A. Biochemistry 1999;38:8022–31.
Rishavy MA, Berkner KL. Biochemistry 2008;47:9836–46.
Cassidy CS, Lin J, Frey PA. Biochemistry 1997;36:4576–84.
Lin J, Westler WM, Cleland WW, Markley JL, Frey PA. Proc Natl Acad Sci USA
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Tobin JB, Whitt SA, Cassidy CS, Frey PA. Biochemistry 1995;34:6919–24.
Reinhardt LA, Sacksteder KA, Cleland WW. J Am Chem Soc 1998;120:13366–9.
Kuhn P, Knapp M, Soltis SM, Ganshow G, Thoene M, Bott R. Biochemistry
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Frick L, Yang C, Marquez VE, Wolfenden RV. Biochemistry 1989;28:9423–30.
Xiang S, Short SA, Wolfenden R, Carter CW Jr., Biochemistry 1995;34:4516–23.
Tronrud DE, Monzingo AF, Matthews BW. Eur J Biochem 1986;157:261–8.
Holden HM, Tronrud DE, Monzingo AF, Weaver LH, Matthews BW. Biochemistry 1987;26:8542–53.
Kim H, Lipscomb WN. Biochemistry 1990;29:5546–55.
Kim H, Lipscomb WN. Biochemistry 1991;30:8171–80.
Poi MJ, Tomaszewski JW, Yuan C, Dunlap CA, Andersen NH, Gelb MH, et al.
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Ramaswamy S, Park D-H, Plapp BV. Biochemistry 1999;38:13951–9.
Sekhar VC, Plapp BV. Biochemistry 1990;29:4289–95.
Thoden JB, Wohlers TM, Fridovich-Keil JL, Holden HM. Biochemistry
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Belogurov GA, Fabrichniy IP, Pohjanjoki P, Kasho VN, Lehtihuhta E, Turkina
MV, et al. Biochemistry 2000;39:13931–8.
Heikinheimo P, Tuominen V, Ahonen A-K, Teplyakov A, Cooperman BS, Baykov

AA, et al. Proc Natl Acad Sci USA 2001;98:3121–6.
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56. Liebschner D, Elias M, Moniot S, Fournier B, Scott K, Jelsch, C, et al. J Am Chem
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Stabilities and Reactivities of Carbocations
RORY MORE O’FERRALL
School of Chemistry and Chemical Biology, University College Dublin, Belfield,
Dublin 4, Ireland
1 Introduction 19
2 Stabilities of carbocations 21
Measures of stability 21
Equilibrium measurements of pKR 28
Kinetic methods for determining pKR 30
Arenonium ions 37
Alkyl cations 46
Vinyl cations 48
The methyl cation: a correlation between solution and the gas phase
Oxygen-Substituted carbocations 51
Metal-Coordinated carbocations 64
Carbocations as protonated carbenes 68
Halide and azide ion equilibria 71
3 Reactivity of carbocations 76
Nucleophilic reactions with water 77
Reactions with water as a base 87
Reactions of nucleophiles other than water 90

Reactivity, selectivity, and transition state structure 105
Hard and soft nucleophiles 110
Summary and conclusions 112
Acknowledgments 114
References 114

1

49

Introduction

There have been a number of reviews of carbocation chemistry in the past 10
years,1–11 including a volume of essays marking the 100th anniversary of the
subject.1 That volume illustrates the variety of structures and reactions that
characterize carbocations. It is this variety which suggests scope for a further
study, namely of the stability and reactivity of carbocations in (mainly) aqueous solution. Dedication to AJ Kresge is appropriate. He has pioneered the
quantitative characterization of reactive intermediates in water as solvent. If he
is best known for his work on enolic species, his steady referencing throughout
this chapter reflects the breadth of his influence in physical organic chemistry.

19
ADVANCES IN PHYSICAL ORGANIC CHEMISTRY
VOLUME 44 ISSN: 0065-3160 DOI: 10.1016/S0065-3160(08)44002-9

Ó 2010 Elsevier Ltd.
All rights reserved


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20

R. MORE O’FERRALL

Attempts to measure the stabilities of carbocations are not new. Hughes and
Ingold established the essential features of solvolysis reactions in the 1930s.12
They identified the SN1 mechanism as involving the formation of a carbocation intermediate and recognized that the rate of solvolysis reflects the stability
of that carbocation. For more than 80 years, rate constants of solvolyses have
provided measures of stability (with allowance for variations in the stability of
reactants).13 Only recently have the stabilities of more than mildly reactive
carbocations, accessible by direct equilibrium measurements,14–16 been determined. Indeed the emergence of gas-phase ion chemistry and new techniques
of mass spectrometry in the 1980s led to a wider knowledge of the stabilities of
carbocations in the gas phase than in solution.2,17
The extension of equilibrium measurements to normally reactive carbocations in solution followed two experimental developments. One was the
stoichiometric generation of cations by flash photolysis or radiolysis under
conditions that their subsequent reactions could be monitored by rapid recording spectroscopic techniques.3,4,18–20 The second was the identification of
nucleophiles reacting with carbocations under diffusion control, which could
be used as clocks for competing reactions in analogy with similar measurements of the lifetimes of radicals.21,22 The combination of rate constants for
reactions of carbocations determined by these methods with rate constants for
their formation in the reverse solvolytic (or other) reactions furnished the
desired equilibrium constants.
Important contributors to these developments were McClelland and Richard,
who have published reviews of their own and related studies.3–8 The present
chapter will focus on recent work therefore and present earlier results mainly
for comparison with new measurements. It will consider two further methods for
deriving equilibrium constants: (a) from kinetic measurements where the reverse
reaction of the carbocation is controlled by diffusion or relaxation of solvent
molecules23–25 and (b) from a correlation of solution measurements with the more
extensive measurements of stabilities of carbocations in the gas phase.26 It will

also show that stabilities of highly reactive carbocations can be determined from
measurements of protonation and hydration of carbon–carbon double bonds.
The existence of equilibrium measurements today usually implies access to a
rate constant for direct reaction of the carbocation with a nucleophile or base.
The chapter will also consider reactivity and selectivity for these reactions. This
area too has been well studied and reviewed,3–8 especially by Mayr’s group
in Munich, who have made extensive recent contributions to the field.27–31
It should be admitted that the author’s own work25,26,32 will be a further focus
for the chapter, which in part will be an ‘‘account of research,’’ and indeed an
update of an earlier multiauthored review.9 The chapter begins, however, with a
digression on the significance of different measures of the stabilities of carbocations. This is followed by a discussion of the use of a solvent free energy
relationship to extrapolate equilibrium and kinetic measurements in concentrated solutions of strong acids to a purely aqueous medium. Some readers may


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STABILITIES AND REACTIVITIES OF CARBOCATIONS

21

wish to omit these sections. However, throughout the first third of the chapter
experimental results are presented in the context of methods used for measurements. The emphasis on methods is followed by discussions of oxygen substituent effects, coordination of metal ions, protonations of carbenes, and
equilibria for the reactions of carbocations with halide or azide ions. The
discussion of reactivity concludes the chapter.

2

Stabilities of carbocations

MEASURES OF STABILITY


The choice of equilibrium constant for measuring the stability of a carbocation
depends partly on experimental accessibility and partly on the choice of
solvent. A desire to relate measurements to the majority of existing equilibrium
constants implies the use of water as solvent. Water has the advantage and
disadvantage that it reacts with carbocations. It follows that the most widely
used equilibrium constant is that for the hydration reaction shown in Equation
(1), which is denoted KR (or pKR). A simple interpretation of KR is that it
measures the ratio of concentrations of unionized alcohol to carbocation in an
(ideal) solution of aqueous acid of concentration 1 M.
Rỵ ỵ 2H2 O ẳ ROH7 ỵ H3 Oỵ
KR ẳ

1ị

ẵR OHẵH3 Oỵ
ẵRỵ Š

Nucleophile affinities
As pointed out by Mayr,28 Ritchie,15 and Hine33,34 KR also measures the
relative affinities of Rỵ and H3Oỵ for the hydroxide ion. It can be regarded
as providing a general affinity scale applicable to electrophiles other than
carbocations.33,35 It can also be factored into independent affinities of Rỵ
and H3Oỵ as shown in Equations (2) and (3). Such equilibrium constants
have been denoted Kc by Hine.33 KR corresponds to the ratio of constants
for reactions (2) and (3) and, in so far as Kc for H3Oỵ is the inverse of Kw the
autoprotolysis constant for water, KR = KcKw
Rỵỵ HO ẳ ROH
Kc ẳ


ẵROH
ẵRỵ ẵHO Š

ð2Þ


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22

H3 Oỵ ỵ HO ẳ 2H2 O

R. MORE OFERRALL

3ị

A distinction between the reactions of Rỵ and H3Oỵ is that while Rỵ reacts
with hydroxide ion in an associative process, H3Oỵ reacts by transfer of a
proton. The difference corresponds to that between the product-forming step
of an SN1 mechanism and an SN2 reaction. Many carbocations are capable of
existing in solution independently of a nucleophile, but this is not true of
highly reactive electrophiles such as Hỵ (or, e.g., CHỵ
3 ) reactions of which
involve breaking as well as making a bond to a nucleophile.
If we focus on Hỵ rather than H3Oỵ, affinities for nucleophiles (bases) must
be expressed relative to a suitable reference. In principle, the familiar equilibrium constants Ka and Kb measure affinities relative to water and hydroxide
ion, respectively [Equations (4) and (5)].
AH ỵ H2 O ẳ A ỵ H3 Oỵ

4ị


A ỵ H2 O ẳ AH ỵ HO

5ị

In practice, it is perhaps unfortunate that the complementary character of the
KR and Ka scales is somewhat obscured by the formulation of Ka as a measure
of acidity, so that the appropriate measure of affinity (in this case basicity) is 1/
K a.
For carbocations, an electrophilicity (Lewis acidity) scale can be based on
ions other than the hydroxide ion as is shown in general for XÀ in Equation
(6), for which the equilibrium constant can be denoted K X
R . Scales based
on chloride ion, for example, have been used in the gas phase2,17,36 and are
also appropriate for nonaqueous solvents.
Rỵ ỵ X ẳ RX

6ị

A further popular scale in the gas phase is hydride ion affinity (HIA)2,37 for
which XÀ = HÀ.
To avoid dealing explicitly with HÀ, this scale is conveniently referenced to a
particular ion such as CHỵ
3 as in Equation (7). Commonly HIAs are expressed
as free energies rather than pKs.
Rỵ ỵ CH4 ẳ R H ỵ CH3ỵ

7ị

The hydride affinity scale is also applicable to aqueous solution. In analogy

with KR we can take H3Oỵ as reference as in Equation (8).
Rỵ ỵ H2 ỵ H2 O ẳ RH ỵ H3 Oỵ

8ị


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STABILITIES AND REACTIVITIES OF CARBOCATIONS

23

À
Á
The two scales are readily interconverted and a ratio of KR values K H
R =K R is
given by Equation (9).
KH
ẵR HẵH2 O
R
ẳ
KR
ẵROHẵH2

9ị

The right-hand side of this equation is evaluated in terms of free energies of
formation in aqueous solution at 25°C of R–H, R–OH, H2O, and H2.38
Free energies of formation, hydride ion affinities, and pKR: Is there an
optimum measure of carbocation stability?

The problem arises, which equilibrium constant offers the most effective
measure of carbocation stability? A good discussion of this question has
been provided by Mayr and Ofial,29 who point out that a rigorous comparison
of stabilities is possible only for isomeric cations. Comparisons between
nonisomeric cations depend on the equilibrium chosen for the measurements.
They argue that the appropriate choice depends on the context and imply that
it is not possible to identify a ‘‘best’’ measure of carbocation stability. While
this is certainly true it is worthwhile pursuing further the likelihood that some
equilibria provide better measures of stability than others, and to assess their
effectiveness and limitations.
For carbocations possessing a b-hydrogen atom, an alternative to
nucleophilic affinities is provided by the pKa for dissociation of a proton
to form an alkene. It is rather easy to recognize that a pKa is not always a
good measure of carbocation stability. This is evident from an example
chosen by Mayr and Ofial, namely, the cyclohexadienyl cation, for which
the conjugate base is benzene [Equation (10)]. Thus, if we seek to compare
stabilities of the cyclohexadienyl cation and t-butyl cation [Equation (11)]
in terms of pKas, the difference will strongly reflect the different stabilities
of the carbon–carbon double bonds of their conjugate bases. In this case
comparing values of pKR provides a better measure of stability because a
contribution from the difference between the corresponding alcohols is
smaller.
C6 H7 ỵ ẳ C6 H6 ỵHỵ

10ị

CH3 ị3 Cỵ ẳ CH3 ị2 CẳCH2 ỵ Hỵ

11ị


Of course, to speak of the stability of a double bond implies further equilibria or reference structures with which the energy of the unsaturated molecule
itself is compared. An obvious reference is the saturated hydrocarbon, with
respect to which stability is measured, for example, by a heat of hydrogenation.


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24

R. MORE O’FERRALL

Perhaps less obviously, the hydrocarbon also provides a reference for the
carbocation. It is worthwhile examining the implications of such a reference,
by considering briefly ‘‘thermodynamic’’ measurements of carbocation stabilities
in terms of heats (enthalpies) or free energies of formation. Mayr and Ofial
contrast our ability to measure the relative energies of tertiary and secondary
butyl cations with the significant differences in relative stabilities of secondary
butyl and isopropyl cations derived from different equilibrium measurements,
namely, hydride, chloride, or hydroxide ion affinities. It is convenient to
focus on this example and to assess the effectiveness of hydride affinities for
comparing the stabilities of these three ions.
Extensive measurements of heats of formation of carbocations in the gas
phase exist and there have been more limited measurements in solution for
nonhydroxylic solvents.39 For comparison with equilibrium measurements in
water, however, the most appropriate measurement would appear to be free
energies of formation in aqueous solution. It is fortunate therefore that a
convenient compilation of values of DG°f (aq) at 25°C has been provided by
Guthrie.38 This allows us for example to derive a value of DG°f (aq) for a
carbocation from a measurement of its pKR value, provided that the free
energy of formation of the corresponding alcohol [R–OH in Equation (1)] is

known.
Heats or free energies of formation can be used to compare directly
the energies of isomeric carbocations. Such a comparison is similar to the
more familiar comparisons of energies of isomeric olefins, such as cis- and
trans-butene. It depends on the energies of formation of isomeric molecules or
ions being based on the same combination of elements. Energies of isomerization can also be measured directly, and Bittener, Arnett, and Saunders have
measured the enthalpy of isomerization of secondary to tertiary butyl cations
in CH2Cl2 as solvent.39
It is possible to compare direct measurements of relative stabilities of
isomeric ions with comparisons of nonisomeric ions by use of a ‘‘group
additivity’’ scheme. Group additivity schemes have been developed by Benson
for heats of formation (and other thermodynamic properties) of organic
molecules in the gas phase,40 and by Guthrie to represent free energies of
formation in aqueous solution.38 In both cases, energies of unstrained hydrocarbons accurately correspond to a sum of contributions from primary,
secondary, tertiary, and quaternary carbons CH3, CH2, CH, and C.
Such a scheme can be extended to carbons bearing functional groups (X) by
assigning contributions for CH2X, CHX, and CX. In principle, carbocations
can be included, with the positively charged carbon considered as a functional
group, with characteristic contributions for primary, secondary, and tertiary
cation centers.
For strict additivity, a group scheme implies that the influence of a
functional group does not extend beyond the carbon atoms adjacent to the
functionalized atom, that is, in our case the carbon bearing the positive charge.