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Lewis Basicity and Affinity Scales

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Lewis Basicity and
Affinity Scales
Data and Measurement

CHRISTIAN LAURENCE
D´epartement de Chimie, Universit´e de Nantes – CNRS, France

JEAN-FRANC
¸ OIS GAL
Institut de Chimie, Universit´e de Nice-Sophia Antipolis – CNRS, France

A John Wiley and Sons, Ltd., Publication

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This edition first published 2010
C 2010 John Wiley & Sons Ltd
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Library of Congress Cataloging-in-Publication Data
Laurence, Christian.
Lewis basicity and affinity scales : data and measurement / Christian Laurence, Jean-Franc¸ois Gal.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-470-74957-9
1. Acids–Basicity. I. Gal, Jean-Franc¸ois. II. Title.
QD477.L38 2009
546 .24–dc22

2009030807

A catalogue record for this book is available from the British Library.
ISBN 9780470749579
Typeset in 10/12pt Times by Aptara Inc., New Delhi, India.
Printed and bound in Great Britain by CPI Antony Rowe, Chippenham, Wiltshire

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To
Eliane
Val´erie, Anne
Hugo, Cl´ement, Simon and Louis
C. Laurence

In memory of my mother
who enabled me to fulfill my vocation as a researcher
J.-F. Gal


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Contents
Preface
1

2

page ix

Lewis Basicity and Affinity Measurement: Definitions and Context
1.1 The Brăonsted Definition of Acids and Bases
1.2 Scales of Brăonsted Basicity and Affinity in Solution
1.3 Scales of Brăonsted Basicity and Affinity in the Gas Phase
1.4 The Lewis Definition of Acids and Bases
1.5 Quantum Chemical Descriptions of Lewis Acid/Base Complexes
1.5.1 Valence-Bond Model
1.5.2 Perturbation Molecular Orbital Theory
1.5.3 Variational Supermolecular Method and Energy
Decomposition Schemes
1.5.4 Natural Bond Orbital Theory
1.5.5 Quantum Theory of Atoms in Molecules
1.6 Measurement of Lewis Basicity
1.6.1 Gas-phase Reactions
1.6.2 Solution Reactions
1.6.3 Standard State Transformations

1.6.4 Choice of Solvent
1.7 Measurement of Lewis Affinity
1.8 The Role of the Solvent
1.9 Spectroscopic Scales of Basicity (Affinity)
1.10 Polybasic Compounds
1.11 Attempts at a Quantitative Formulation of the Lewis Definition
of Acids and Bases
1.11.1 Hard and Soft Acids and Bases
1.11.2 The ECW and ECT Models
1.11.3 The Beta and Xi Equation
1.11.4 A Chemometric Approach
1.11.5 Quantum Chemical Descriptors for Basicity Scales
1.12 Concluding Remarks and Content of Chapters 2–7
References

1
2
3
6
6
10
10
10

The Donor Number or SbCl5 Affinity Scale
2.1 Structure of SbCl5 Complexes
2.2 Definition of the Donor Number Scale
2.3 Experimental Determination of the Donor Number

71

71
73
73

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12
17
18
20
21
22
23
24
24
29
34
38
42
42
47
52
53
56
58
60


viii


Contents

2.4
2.5

The Donor Number Scale: Data
Critical Discussion
References

74
80
81

3 The BF3 Affinity Scale
3.1 Structure of BF3 Complexes
3.2 Definition of the BF3 Affinity Scale
3.3 Experimental Determination of the BF3 Affinity Scale
3.4 The BF3 Affinity Scale: Data
3.5 Discussion
3.5.1 Medium Effects
3.5.2 Hardness of BF3
3.5.3 Comparison of the BF3 and SbCl5 Affinity Scales
3.5.4 Computation of the BF3 Affinity
3.6 Conclusion
References

85
86
88
89

90
102
102
102
103
104
105
106

4 Thermodynamic and Spectroscopic Scales of Hydrogen-Bond
Basicity and Affinity
4.1 Structure of Hydrogen-Bonded Complexes
4.2 Hydrogen-Bond Basicity Scales: Early Works
4.3 The 4-Fluorophenol Hydrogen-Bond Basicity Scale
4.3.1 Definition
4.3.2 Method of Determination
4.3.3 Polyfunctional Hydrogen-Bond Acceptors
4.3.4 Data
4.3.5 Range of Validity of the Scale
4.4 Hydrogen-Bond Affinity Scales: Early Studies
4.5 The 4-Fluorophenol Affinity Scale
4.6 Comparison of 4-Fluorophenol Affinity and Basicity Scales
4.7 Spectroscopic Scales
4.7.1 Infrared Shift of Methanol
4.7.2 Solvatochromic Shifts of 4-Nitrophenol and 4-Nitroaniline
4.8 Conclusion
References

111
113

117
119
119
119
120
121
167
168
170
185
188
188
210
221
221

5 Thermodynamic and Spectroscopic Scales of Halogen-Bond
Basicity and Affinity
5.1 Structure of Halogen-Bonded Complexes
5.2 The Diiodine Basicity Scale
5.2.1 Definition of the Scale
5.2.2 Methods for the Determination of Diiodine
Complexation Constants
5.2.3 Temperature Correction
5.2.4 Solvent Effects
5.2.5 Data

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231
237
237
238
239
239
243


Contents

6

7

ix

5.3 Is the Diiodine Basicity Scale a General Halogen-Bond Basicity Scale?
5.4 The Diiodine Affinity Scale
5.5 Spectroscopic Scales
5.5.1 Infrared Shifts of ICN, I2 and ICl
5.5.2 The Blue Shift of the Diiodine Visible Band
5.6 Conclusion
References

283
285
286
286
306

309
309

Gas-Phase Cation Affinity and Basicity Scales
6.1 Cations as Lewis Acids in the Gas Phase
6.2 Structure of Cation/Molecule Adducts
6.3 Experimental Techniques for Measuring Gas-Phase Cation Affinities
and Basicities
6.3.1 High-Pressure Mass Spectrometry (HPMS)
6.3.2 Collision-Induced Dissociation Threshold (CIDT)
6.3.3 Ligand-Exchange Equilibrium Measurements in Trapping Devices
6.3.4 Selected Ion Flow Tube (SIFT)
6.3.5 Kinetic Method
6.3.6 Radiative Association Kinetics (RAK)
6.3.7 Blackbody Infrared Radiative Dissociation (BIRD)
6.3.8 Vaporization and Lattice Energies
6.4 Ion Thermochemistry Conventions
6.5 Lithium, Sodium, Potassium, Aluminium, Manganese,
Cyclopentadienylnickel, Copper and Methylammonium Cations
Affinity and Basicity Scales
6.5.1 Lithium
6.5.2 Sodium
6.5.3 Potassium
6.5.4 Aluminium
6.5.5 Manganese
6.5.6 Cyclopentadienylnickel
6.5.7 Copper
6.5.8 Methylammonium
6.6 Significance and Comparison of Gas-Phase Cation Scales
6.6.1 Properties of Cations and Significance of MCB and MCA Scales

6.6.2 Relationship of MCA with MCB
6.6.3 The Computation of MCB and MCA Scales
6.6.4 MCA and MCB Scales and the Concept of a Cation/π Interaction
6.6.5 Conventional Versus Ionic Hydrogen-Bond Basicity and
Affinity Scales
6.6.6 Comparison of Cation Basicity Scales
References

323
323
326

The Measurement of Lewis Basicity and Affinity in the Laboratory
7.1 Calorimetric Determination of the BF3 Affinity of Pyridine
by Gas/Liquid Reaction

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334
334
335
336
337
337
338
338
339
339

340

340
346
353
354
354
360
366
371
370
370
381
382
383
386
387
389
401
401


x

Contents

7.1.1

7.2

7.3


7.4

7.5

7.6

7.7

Introduction: Principles and Difficulties in the Calorimetric
Measurement of the Enthalpy of a Gas/Liquid Reaction
7.1.2 Reagents and Equipment
7.1.3 Experiment
7.1.4 Results
Calorimetric Determination of the BF3 Affinity of Pyridine
by Liquid/Liquid Reaction
7.2.1 Introduction: Measuring Relative BF3 Affinity by Ligand
Exchange in Solution
7.2.2 Reagents and Equipment
7.2.3 Experiment
7.2.4 Results
Determination by FTIR Spectrometry of the Complexation Constants
of 4-Fluorophenol with Isopropyl Methyl Ketone and Progesterone
7.3.1 Introduction: Recognition of Progesterone by its Receptor
7.3.2 Reagents and Equipment
7.3.3 Experiment
7.3.4 Results and Discussion
Determination by FTIR Spectrometry of the Complexation Enthalpy
and Entropy of 4-Fluorophenol with Cyclopropylamine
7.4.1 Introduction
7.4.2 Reagents and Equipment

7.4.3 Experiment
7.4.4 Results
7.4.5 Comparison with Theoretical Calculations
FTIR Determination of the OH Shift of Methanol Hydrogen
Bonded to Pyridine, Mesitylene and N -Methylmorpholine
7.5.1 Introduction
7.5.2 Reagents and Equipment
7.5.3 Experiment
7.5.4 Results and Discussion
Solvatochromic Shifts of 4-Nitrophenol upon Hydrogen
Bonding to Nitriles
7.6.1 Introduction
7.6.2 Reagents and Equipment
7.6.3 Experiment
7.6.4 Results and Discussion
Determination of the Complexation Constant of Diiodine
with Iodocyclohexane by Visible Spectrometry
7.7.1 Introduction: Measuring the Weak Diiodine Basicity
of Haloalkanes
7.7.2 The Rose–Drago Method
7.7.3 Reagents and Equipment
7.7.4 Experiment
7.7.5 Results and Discussion: Illustration of the HSAB Principle

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401
403
404
405

406
406
407
407
407
408
408
409
409
410
413
413
414
414
414
417
418
418
418
419
419
420
420
421
421
422
424
424
424
426

426
427


Contents

7.8 Determination of the Complexation Enthalpy and Entropy of Diiodine
with Dimethyl Sulfoxide by Visible Spectrometry
7.8.1 Introduction
7.8.2 Reagents and Equipment
7.8.3 Experiment
7.8.4 Results
7.8.5 Discussion
7.9 FTIR Determination of the Shift of the I C Stretching of Iodine
Cyanide upon Halogen Bonding to Phosphine Chalcogenides
7.9.1 Introduction
7.9.2 Reagents and Equipment
7.9.3 Experiment
7.9.4 Results and Discussion: ∆ν(ICN) as a Spectroscopic Scale
of Halogen-Bond Affinity
7.10 Blue Shift of the Visible Diiodine Transition Upon Halogen
Bonding to Pyridines
7.10.1 Introduction
7.10.2 Reagents and Equipment
7.10.3 Experiment
7.10.4 Results and Discussion: Substituent Effects
7.11 Mass Spectrometric Determination of the Gas-Phase Lithium Cation
Basicity of Dimethyl Sulfoxide and Methyl Phenyl Sulfoxide by the
Kinetic Method
7.11.1 The Kinetic Method

7.11.2 Reagents and Equipment
7.11.3 Experiment
7.11.4 Data Treatment
7.11.5 Discussion: Substituent Effects
References
Index

xi

429
429
429
429
430
432
434
434
435
435
435
436
436
437
437
438

439
439
440
441

442
444
445
447

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Preface
In 1923, G.N. Lewis proposed an electronic definition of acids and bases founded on
electron pair sharing. Compared with the protonic definition of Brăonsted based on proton
exchange, the new Lewis definition broadened considerably the field of acid/base reactions.
It incorporates heterolysis, coordination, solvation, complexation, hydrogen-bond formation, halogen-bond formation and electrophilic and nucleophilic reactions into acid/base
chemistry. It is therefore not surprising that discussions of Lewis acidity and Lewis basicity
appear in almost every textbook on general, organic and inorganic chemistry.
A major criticism, however, is often made of the Lewis definition. Contrary to the
Brăonsted definition, it is not possible to establish any universal order of acid or base strength.
In the Brăonsted definition, the proton is used as the reference and the quantitative study of
proton exchange reactions between bases, by means of electrochemical or spectrometric
methods, enabled the strength of several thousand Brăonsted acids and bases to be measured
unambiguously. Thermodynamic databases for proton exchange in the gas phase (NIST
webbook, .) or in water (e.g. D.D. Perrin, Dissociation Constants
of Organic Bases in Aqueous Solution, Butterworths, London, 1965, and supplement,
1972) are therefore extremely useful in analytical, organic and inorganic chemistry and in
biochemistry.
In contrast, in the Lewis definition there is no single reference that is naturally operational.
Since there is no obvious reason to choose one reference rather than another, there are

potentially as many acidity or basicity scales as possible references.
Concerning basicity, however, which is the subject of this book, the statistical treatment
of various scales of Lewis basicity, as well as theoretical studies, show that a limited number
of factors influence the strength of Lewis bases. Consequently, the judicious choice of a
few reference Lewis acids should allow Lewis basicity scales to be constructed and used as
a general guide to basicity. Although none of these scales can be considered as universal,
each will have a domain of validity that is sufficiently wide to be useful in many branches
of chemistry and biochemistry.
It is with this objective that this book presents thermodynamic and spectroscopic data on
the strength of Lewis bases coming from both the literature and our laboratories. We do not
aim to provide exhaustive scales but rather a selective guide. From a mass of data, sometimes
contradictory and often lacking consistency, we have chosen typical reference Lewis acids.
These are SbCl5 , BF3 , 4-FC6 H4 OH, CH3 OH, 4-NO2 C6 H4 OH, 4-NO2 C6 H4 NH2 , I2 , ICl,
ICN, Li+ , Na+ , K+ , Al+ , Mn+ , CpNi+ , Cu+ and CH3 NH+
3 . This choice is justified in
the first chapter. For each of these acids, we have selected only the data determined
by the most accurate techniques and/or the most reliable methods. In cases of doubt,
some measurements from the literature have been repeated in our laboratories. Additional
measurements have also been carried out in order to fill significant gaps. Finally, data have

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xiv

Preface

been made homogeneous either by means of the usual thermodynamic relationships, in
order to refer to the same standard state and to the same temperature, or by means of
extrathermodynamic relationships, specifically established, in order to refer them to the

same solvent. In all, more than 2400 equilibrium constants of acid/base reactions, and thus
of Gibbs energies, about 1500 complexation enthalpies and, for spectroscopic scales, nearly
2000 infrared and ultraviolet shifts of absorption bands upon complexation are gathered
together in this book.
We expect that this collection of data will enable experimental chemists to understand
and predict better the numerous chemical, physical and biological properties that depend
upon Lewis basicity. Indeed, basicity parameters can be introduced as explanatory variables
in many linear free energy relationships, linear solvation energy relationships, structure–
property relationships and structure–biological activity relationships.
Chemometricians may be able to construct many kinds of data matrices from the Lewis
basicity scales in this book. For example, matrices might refer to a given family of bases
(e.g. nitriles), or a given property (e.g. complexation enthalpies), or a given type of complex
(e.g. hydrogen-bonded complexes), or a combination of families, properties and types of
complexes. The analysis of judiciously constructed matrices by appropriate chemometric
methods should enable the intrinsic fundamental effects in the data matrix to be extracted
and used to predict the Lewis basicity and many basicity-dependent properties.
In addition, measured experimental basicities and affinities are essential to computational
chemists for the validation, calibration and establishment of reliable computational methods
for quantifying and explaining intermolecular forces and the chemical bond. In fact, the
formation of Lewis acid/base adducts covers a wide variety of bond-forming processes
from the weak hydrogen bond to the strong dative bond or ion/molecule bond.
Scepticism about the quantitative usefulness of the Lewis concept of acids and bases is
still frequently encountered in chemistry textbooks. We expect that this book will demonstrate that quantitative data exist for acid/base systems other than those involving proton
donors and acceptors, and will encourage textbook authors to go beyond a mere qualitative
presentation of the Lewis acid/base concepts.
The hope for a quantitative Lewis acid/base chemistry has motivated our research at
the Universities of Nantes and Nice-Sophia Antipolis for more than 40 years. During this
long period, many people have contributed to this research. We thank our colleagues in
Nantes and Nice (M. Berthelot, J. Graton, M. Helbert-Nicolet, B. Illien, J.-Y. Le Questel,
P.C. Maria and P. Nicolet) for their generous help, the technical staff of our laboratories

(F. Besseau, M. Decouzon, M. Luc¸on and A. Planchat) for their skillful assistance and our
post-doctoral, PhD and Master’s Degree students, whose names appear in the references,
for their efforts.
We especially acknowledge the following collaborations. Prof. Michel Berthelot contributed very significantly to the construction of the following scales: 4-fluorophenol basicity and affinity, diiodine basicity, methanol, I2 and ICl shifts. Most of the 4-fluorophenol
affinity values were obtained by Franc¸ois Besseau. Dr Mich`ele Decouzon dedicated much
time to the maintenance of and measurements made with the FTICR mass spectrometer
in Nice. Dr Mohamed Jamal El Ghomari (Marrakech) contributed to a first version of
the diiodine basicity scale. Dr Maryvonne Helbert carried out the measurements of the
methanol, I2 and ICl spectroscopic shifts and many diiodine and 4-fluorophenol complexation constants. Dr Josef Kaczmarek (Gdansk) carried out the measurements of the ICN

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Preface

xv

spectroscopic shifts. Dr Maryvonne Luc¸on measured many diiodine complexation constants and IR shifts of 4-nitroaniline, constructed the methanol, pyrrole and cyanoacetylene
affinity and basicity scales and recorded the FTIR and UV spectra of laboratory experiments 7.3 to 7.10. Prof. Pierre-Charles Maria participated very actively in the development
of the BF3 affinity and lithium cation basicity scales. Dr Raphael Notario and Prof. Jose
Luis Abboud (Madrid) helped in the construction of the diiodine basicity scale. Prof. Pierre
Nicolet co-directed the work on the 4-nitrophenol and 4-nitroaniline solvatochromic scales.
Prof. Ewa Raczyñska (Warsaw) studied the hydrogen-bond basicity of amidines and other
bases. Prof. Manuel Y´an˜ ez (Madrid) performed high-level ab initio calculations on Al+ ,
Mn+ and CpNi+ complexes in order to anchor the corresponding affinity and/or basicity
scales.
The electronic version of the manuscript was produced entirely by Dr Maryvonne Luc¸on.
Dr Charly Mayeux prepared the figures illustrating the 3D geometry of the complexes. Mrs
Carol Robins revised the English of the whole manuscript. We wish to express our gratitude
to them for their assistance in the preparation of this book.

We have benefited from the consummate professionalism of the editorial staff at Wiley.
It was a pleasure to work with all of them.
Finally, without the understanding and patience of our wives, Eliane and Juliette, we
could never have accomplished this work.

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1
Lewis Basicity and Affinity
Measurement: Definitions
and Context
Two definitions of acids and bases are used nowadays, the Brăonsted definition and the
Lewis definition. This book deals with the quantitative behaviour of Lewis bases. However,
since Lewis bases are also Brăonsted bases, this chapter begins with a short presentation of
the Brăonsted definition and of the quantitative behaviour of Brăonsted bases [1]. The Lewis
definition and the many ways for its quantification will then be studied. This introductory
chapter is intended to help in the understanding and use of the tables in Chapters 2–6,
which contain quantitative data on Lewis basicity and affinity, and not to discuss the Lewis
acid/base concept in depth. This subject has been excellently treated in a book [2] and a
review [3] by Jensen, and books and chapters by Mulliken and Person [4], Gur’yanova et al.
[5], Drago [6], Finston and Rychtman [7] and Weinhold and Landis [8], to quote just a few.
As far as possible, we have followed the IUPAC recommendations for the names and
symbols of physical and chemical quantities ( and have used the
international system of units (SI) and the recommended values of the fundamental physical
constants ( Units that are not part of the SI have been used
˚ = 10−10 m),

in appropriate contexts. These are: litre (1 l = 103 m3 ), a ngstrăom (1 A
−19
−30
J),
Debye
(1
D
≈
3.336
×
10
C m) and bar
electronvolt (1 eV ≈ 1.602 18 × 10
(1 bar = 105 Pa).
In tabulating thermodynamic and spectroscopic basicity scales, 1 : 1 complexation constants, Gibbs energies, enthalpies, entropies and ultraviolet (UV) and infrared (IR) spectral
shifts are therefore given in l mol−1 (identical with dm3 mol−1 ), kJ mol−1 , J K−1 mol−1 and
cm−1 , respectively. Logarithms of equilibrium constants (log K) are to base 10 and without
units since the calculated quantity is log (K/1 l mol−1 ).
In naming compounds, we have not always followed the nomenclature rules. We have
sometimes preferred the common name found in most chemical catalogues. For clarity, the
Lewis Basicity and Affinity Scales: Data and Measurement
C 2010 John Wiley & Sons, Ltd

Christian Laurence and Jean-Franc¸ois Gal

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2


Lewis Basicity and Affinity Scales

Table 1.1 Symbols for families of Lewis bases used in the graphs.
Family
Carbon π bases
Aromatics,
alkenes,
alkynes
Oxygen bases
Single-bonded
Carbonyls
Sulfinyls
Phosphoryls,
arsine oxides
N-Oxides
Nitros, sulfonyls

Symbol

Family

Symbol

×

Nitrogen bases
sp-Hybridized

sp2 -Hybridized
sp3 -Hybridized

Phosphorus,
arsenic bases
Sulfur bases
Single-bonded

Family

Symbol

Selenium bases
Single-bonded,
seleno-carbonyls,
selenophosphoryls
−

Halogen bases
Fluoroalkanes

+

Chloroalkanes
Bromoalkanes

Thiocarbonyls
Thiophosphoryls

Iodoalkanes
Miscellaneous bases

name is followed, in most tables in Chapters 2–6, by a formula that allows the drawing of

the structure, or by the drawing itself.
In the graphs, in order to facilitate the identification of family-dependent trends, bases
are labelled as summarized in Table 1.1, unless otherwise stated in the legend of the
graph.

1.1

The Brăonsted Definition of Acids and Bases

A powerful definition of acids and bases was proposed in 1923 by J.N. Brăonsted [9], namely
an acid is a species capable of donating a proton, and a base is a species capable of accepting
a proton. This can be expressed by the scheme
A

B + H+

(1.1)

where the acid A and the base B are termed a conjugate acid/base pair. Equation 1.1
represents a hypothetical scheme used for defining an acid and a base rather than a reaction.
Indeed, reaction 1.1 cannot actually occur in a solvent because the bare proton H+ cannot
exist in solution, and cannot be studied directly in the gas phase because of the extremely
large endoergic values involved.
The only reactions between Brăonsted acids and Brăonsted bases that can be observed in
solution and studied directly in the gas phase are reactions of proton exchange between two
conjugate acid/base pairs A1 /B1 and A2 /B2
A1 + B2

A2 + B1


(1.2)

For example, in aqueous solutions, the acid CH3 COOH reacts with water acting as a base:
CH3 COOH + H2 O

H3 O+ + CH3 COO−

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(1.3)


Lewis Basicity and Affinity Measurement: Definitions and Context

3

Table 1.2 Some types of neutral Bronsted
acidsa .
ă
O H acids
Inorganic oxyacids
Carboxylic acids
Phenols, alcohols, water
N H acids
C H acids
S H acids
X H acids
a

HNO3 , H2 SO4 , H3 PO4 , HClO4

RCOOH
ArOH, ROH, H2 O
ArNH2 , RSO2 NH2 , RCONH2 , HNCS, HNCO, HN3
HC N, RC CH, HC(NO2 )3
ArSH, H2 S
HF, HCl, HBr, HI

In the formulae, R is an alkyl group and Ar an aryl group.

and the base NH3 reacts with water acting as an acid:
H2 O + NH3

−
NH+
4 + OH

(1.4)

In the gas-phase reaction 1.5, the proton is exchanged between the ammonium
ion/ammonia and the pyridinium ion/pyridine pairs:
NH+
4 + C5 H5 N

C5 H5 NH+ + NH3

(1.5)

Any compound containing hydrogen can, in principle, be regarded as a Brăonsted acid,
but in many of them (e.g. most hydrocarbons) the tendency to lose a proton is so small that
they do not show acidic behaviour under ordinary conditions. Examples of neutral Brăonsted

acids are given in Table 1.2.
The same kind of practical restriction should be applied to Brăonsted bases. Neutral
molecules or atoms can attach a proton in the gas phase because of the tremendous acidity
of the bare proton: even rare gases may be protonated in the gas phase. For the liquid phase,
superacid systems (such as HF/SbCl5 that are more acidic than 100% sulfuric acid) can
also protonate many molecules [10]. For example, the protonated form of methane, CH5 + ,
which was discovered in the gas phase by mass spectrometry in the 1950s, has also been
reported in superacid solutions. However, the important bases in chemistry are (i) anions
and (ii) molecules containing elements of groups 15 and 16 with unshared electron pair(s).

1.2

Scales of Brăonsted Basicity and Affinity in Solution

Brăonsted definitions are easily translated into quantitative measurements. The equilibrium
constant of reaction 1.2, K = (A2 )(B1 )/(A1 )(B2 ), where parentheses denote activities, is
equal to the ratio of the hypothetical constants (B1 )(H+ )/(A1 ) and (B2 )(H+ )/(A2 ). K will
therefore measure the ratio of the acid strengths of A1 and A2 , or the ratio of the base
strengths of B2 and B1 . Since these two ratios are equal, it is not necessary to give separate
definitions of base strength and acid strength. The base strength of any base B is usually
given by the acid strength of its conjugate acid A. Thus, for the pair C5 H5 NH+ /C5 H5 N, the
base strength of pyridine is described in terms of the acid strength of the pyridinium ion.
It is not possible to measure the absolute strength of an acid or base in solution but
strengths can be measured relative to some standard pair, A◦ /B◦ . The acid strength of the

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4


Lewis Basicity and Affinity Scales

studied pair, A/B, is then given by the equilibrium constant of the reaction
A + B◦

A◦ + B

(1.6)

The standard pair, A◦ /B◦ , is usually chosen to be the acid/base pair of the solvent. In
aqueous solutions, the pair H3 O+ /H2 O is commonly preferred to the other possible pair,
H2 O/OH− . The strength of any acid A is then measured by the equilibrium constant of the
reaction
A + H2 O

H3 O+ + B

(1.7)

When measurements are made in dilute aqueous solution, the concentration of water
remains essentially constant and its activity can be taken as unity. The strength of the acid
A is then measured by the acid dissociation constant:
K a = (B) (H3 O+ )/(A)

(1.8)

The strength of a neutral base B is described in terms of the K a of its conjugate acid BH+ ,
usually denoted K BH+ :
K BH+ = (B) (H3 O+ )/(BH+ )


(1.9)

Since the observed equilibrium constants vary over many powers of 10, the convention to
use the operator p ≡ −log10 was adopted, leading to the quantity pK BH+ :
pK BH+ = − log10 K BH+

(1.10)

Clearly, a large positive value of pK BH+ describes a strong and a small or negative value
describes a weak Brăonsted base.
Tables of pK BH+ in aqueous solution have been compiled by Perrin [11]. They cover
the literature until 1972 and contain more than 7000 organic bases, mainly sp2 and sp3
nitrogen bases. Many of the carbon, oxygen, sulfur and sp nitrogen bases are not protonated
in dilute acid solutions, so that solutions with variable concentrations of a strong acid
have to be used. In such media, K BH+ values cannot be calculated without formulating
some extrathermodynamic assumption. The pK BH+ values of many weak bases have been
carefully measured by Scorrano et al. [12–21]. Table 1.3 gives selected pK BH+ values.
The pK BH+ is directly converted into the Gibbs energy change of the proton exchange as
follows:
∆G ◦ = ln(10)RTpK BH+

(1.11)

The literature is poorer in enthalpies of proton exchange reactions. However, Arnett
et al. have established an enthalpic scale of Brăonsted basicity [2225] (i.e. a Brăonsted
affinity scale) from the heats of protonation of many bases in fluorosulfuric acid. The heats
of protonation (ionization), ∆H i , correspond simply to the heat of transfer of the base
from infinite dilution in the inert solvent CCl4 to infinite dilution in the (often) completely
protonating solvent HSO3 F. A surprisingly good correlation (r = 0.986, n = 55, s =
5.4 kJ mol−1 ) is obtained [23] between the enthalpies of protonation and the corresponding

aqueous pK BH+ values. Selected values of ∆H i are given in Table 1.3.

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Lewis Basicity and Affinity Measurement: Definitions and Context

5

Table 1.3 Thermodynamic parameters for protonation of organic bases: pK BH+ in water,
∆Hi (kJ mol−1 ) in fluorosulfuric acid and GB and PA (kJ mol−1 ) in the gas phase.
Base
Hexamethylbenzene
Methylamine
Ethylamine
Dimethylamine
Diethylamine
Di-n-butylamine
Trimethylamine
Triethylamine
Tri-n-butylamine
Quinuclidine
Triphenylamine
3,5-Dichloropyridine
2-Bromopyridine
2-Chloropyridine
3-Bromopyridine
Quinoline
Pyridine
4-Methylpyridine

2,6-Dimethylpyridine
2,4,6-Trimethylpyridine
Aniline
N,N-Dimethylaniline
Methanol
Ethanol
Water
Dimethyl ether
Diethyl ether
Tetrahydrofuran
Benzaldehyde
Acetophenone
Benzophenone
Acetone
Diethyl ketone
Dicyclopropyl ketone
Methyl acetate
Methyl propionate
Methyl benzoate
N,N-Dimethylacetamide
N,N-Dimethylformamide
N-Methylpyrrolidone
Tetramethylurea
Dimethyl sulfoxide
Hexamethylphosphoric triamide
Triphenylphosphine oxide
Pyridine N-oxide
Nitrobenzene
N,N-Dimethylthioacetamide
Methyl sulfide

Ethyl sulfide
Triphenylphosphine

pK BH+
−14.65
10.65
10.68
10.78
11.02
11.25
9.80
10.72
9.93
11.15
0.67
0.90
0.72
2.85
4.85
5.20
6.03
6.72
7.43
4.60
5.15
−2.05
−1.94
−1.74
−2.48
−2.39

−4.48
−3.87
−4.71
−3.06
−3.88
−2.40
−3.90
−4.37
−7.05
−0.21
−1.13
−0.71
−0.14
−1.54
−0.97
0.8
−2.25
−6.99
−6.68

−∆Hi
193.9
195.9
197.4
199.5
194.1
196.8
205.7
189.2
191.6

79.9
128.4
126.2
132.5
144.9
150.9
161.3
163.4
170.3
178.5
142.3
157.7
79.9
68.6
79.8
82.0
67.4
79.1
70.7
79.9
87.0

133.9
123.4
131.0
157.3
119.7
87.4
139.7
27.6

79.5
120.0

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GB

PA

836.0
864.5
878.0
896.5
919.4
935.3
918.1
951.0
967.6
952.5
876.4

860.6
899.0
912.0
929.5
952.4
968.5
948.9
981.8
998.5

983.3
908.9

873.0
869.0
878.2
921.4
898.1
915.3
931.1

904.8
900.9
910.0
953.2
930.0
947.2
963.0

850.6
909.2
724.5
746.0
660.0
764.5
801.0
794.7
802.1
829.3
852.5

782.1
807.0
850.6
790.7
799.2
819.5
877.0
856.6
891.6
899.6
853.7
928.7
876.4
892.9
769.5
894.4
801.2
827.0
940.4

882.5
941.1
754.3
776.4
691.0
792.0
828.4
822.1
834.0
861.1

882.3
812.0
836.8
880.4
821.6
830.2
850.5
908.0
887.5
923.5
930.6
884.4
958.6
906.2
923.6
800.3
925.3
830.9
856.7
972.8


6

1.3

Lewis Basicity and Affinity Scales

Scales of Brăonsted Basicity and Affinity in the Gas Phase


Various mass spectrometric techniques permit the study of proton transfer reactions in the
gas phase and the definition of Brăonsted basicity scales free of solvent effects [26].
The gas-phase basicity GB and the proton affinity PA of a base B are defined as the
standard Gibbs energy change and the standard enthalpy change, respectively, of the formal
deprotonation reaction 1.12:
BH+ → B + H+
∆H ◦ = proton affinity = PA
∆G ◦ = gas-phase basicity = GB

(1.12)

Unfortunately, this terminology, currently in use, is not completely correct since an affinity
is a chemical potential (a ∆G value) whereas the proton affinity is an enthalpy. An alternative
terminology for ∆H ◦ might be ‘enthalpy of basicity’, but it seems unrealistic to propose a
change of terminology now considering the accepted practice.
The absolute basicity and affinity cannot be obtained directly because the gas-phase
reaction 1.12 is extremely endoergic and endothermic. It is common practice to resort to
thermodynamic cycles, involving enthalpies of formation and dissociation thresholds, to
calculate absolute PAs. The transformation of absolute PAs into absolute GBs (Equation
1.13) requires the evaluation of the entropy of basicity (Equation 1.14) (mainly through
quantum chemical calculations today):
GB = PA − T ∆S ◦
∆S ◦ = S ◦ (B) + S ◦ (H+ ) − S ◦ (BH+ )

(1.13)
(1.14)

The number of absolute PA and GB values that can be accurately evaluated is very
limited. In fact, most parts of the scales are obtained by measuring the relative basicity of
an unknown using a reference base B◦ of known GB. Relative basicities, designated ∆GB,

are obtained from equilibrium constants K of the proton exchange reaction 1.15 between
bases B and B◦ :
BH+ + B◦

B◦ H+ + B
∆GB = −RT lnK = GB(B) − GB(B◦ )

(1.15)
(1.16)

The known basicities span a very wide range of about 1300 kJ mol−1 from He to Cs2 O.
However, the basicity of the majority of organic bases falls within 700–1000 kJ mol−1 . A
selection is presented in Table 1.3. Thousands of PA and GB values have been critically
compiled by Hunter and Lias [27, 28].

1.4

The Lewis Definition of Acids and Bases

In the original Lewis definition (1923 [29], 1938 [30]), acids are electron-pair acceptors
and bases are electron-pair donors. The fundamental reaction between a Lewis acid A and
a Lewis base B is the formation of a complex (or adduct or coordination compound or
addition compound) A–B (reaction 1.17):
A + :B

A–B

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(1.17)



Lewis Basicity and Affinity Measurement: Definitions and Context

7

In this reaction, the unshared electron pair of the base forms a coordinate covalent bond (or
dative bond or dipolar bond) with an electron-deficient atom of the acid. The archetype of
a Lewis acid/base reaction is
BF3 + : NH3

F3 B–NH3

(1.18)

BF3 is a Lewis acid because the boron atom has only six electrons in its valence shell and,
having room for eight, can accept the lone pair of the nitrogen atom of ammonia.
The proton is a Lewis acid because it can accept an electron pair into its empty 1s atomic
orbital. It follows that all Brăonsted bases are Lewis bases. All Brăonsted acids are also Lewis
acids because they are hydrogen-bond donors, that is, electron acceptors (see below).
However, a much wider range of species can be classified as Lewis acids than can be
classified in the Brăonsted scheme. The translation of Lewis’s definition into quantummechanical terms by Mulliken (1952) [31] further widened the definition, so as to include
those reagents that donate or accept a fraction, possibly very small, of an electron. With
this extension, the compounds in Tables 1.4 and 1.5 are considered as Lewis acids (electron

Table 1.4 Examples of Lewis acids.
Metals: M
Cations
Proton: H+
Metallic: Mn+

Organometallic: CH3 Hg+
Halogens: I+
Carbocations: CH3 +
Covalent metal halides, hydrides or alkyls: MX n , MHn , MRn
Group 4: TiCl4
Group 8: FeCl3
Group 12: ZnCl2 , CdI2 , HgCl2
Group 13: BF3 , BCl3 , BH3 , BMe3
AlCl3 , AlMe3
GaCl3 , GaH3 , GaMe3
Group 14: SnCl4
Group 15: SbCl3 , SbCl5
Halogen-bond donors
Dihalogens: I2 , Br2 , Cl2
Interhalogens: ICl, IBr, ClF, BrCl
Organic halogens: IC N, ICF3 , IC CR
Hydrogen-bond donors (Bronsted
acids)
ă
OH: RCOOH, ArOH, ROH, H2 O
NH: RCONH2 , ArNH2 , HNCS
CH: CHCl3 , RC CH
SH: ArSH
XH: HF, HCl
π Acceptors
SO2 , SO3
Ethylenic, acetylenic, aromatic hydrocarbons substituted with electron-withdrawing groups
Quinones

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