Table Of ContentChemical Hardness
Guest-Editor: K.D. Sen
With contributions by
J. A. Alonso, B.G. Baekelandt, L.C. Balbas
P.K. Chattaraj, J.L. Gazqu6z, M.E. Grice
L. Komorowski, N.H. March, W.J. Mortier
J. S. Murray, R.F. Nalewajski, R.G. Parr
R. G. Pearson, P. Politzer, IL A. Schoonheydt
K. D. Sen
With 53 Figures and 52 Tables
galreV-regnirpS
Berlin Heidelberg New kroY
London Paris Tokyo
Hong Kong Barcelona Budapest
:rotidE-tseuG
Professor K. D. Sen
School of Chemistry, University of Hyderabad,
Hyderabad 500 134, India
ISBN 3-540-56091-2 Springer-Verlag Berlin Heidelberg New York
ISBN 0-387-56091-2 Springer-Verlag New York Berlin Heidelberg
This work is subject to copyrighL All rights are reserved, whether the whole or part of the material
is concerned, specifically rite rights of translation, reprinting, re-use of illustrations, recitation,
broadcasting, reproduction on ndcrofilms or in other ways, and storage in data banks. Dublieation
of this publication or parts thereof is only permitted under the provisions of the German Copyright
Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee mustalways be paid.
(cid:14)9 Springer-Verlag Berlin Heidelberg 1993
s in Germany
The use of general descriptive names, trade marks, etc. in this publication, even if the former are
not especially identified, is not to be taken as a sign that such names, as understood by the Trade
Marks and Merchandise Marks Act, may accordingly be used freely by anonyme.
Typ~etting: Maenfillan India Ltd., Bangalore-25, India
printing: Colordruck, Berlin; Bookbindh~g: Lfideritz & Bauer, Berlin
51/3020 - 5 4 3 2 1 0 - Printed on acld-free paper
Editorial Board
Professor MichaelJ. Clarke, Boston College, Department of Chemistry,
Chestnut Hill, Massachusetts 02167, U.S.A.
Professor John B. Goodenough, Center of Materials Science and Engineering,
University of Texas at Austin, Austin, Texas 78712, U.S.A.
Professor James A. lbers, Department of Chemistry, Northwestern University,
Evanston, Illinois 60201, U.S.A.
Professor Christian K. Jorgensen, D6pt. de Chimie Min6rale de l'Universit6
30 quai Ernest Ansermet, CH-1211 Gen6ve 4
Professor David Michael P. Mingos, Imperial College of Science, Technology and
Medicine, Dept. of Chemistry, South Kensington, London SW7 2AY, Great Britain
Professor Joe B. Neilands, Biochemistry Department, University of California,
Berkeley, California 94720, U.S.A.
Professor Graham A. Palmer, Rice University, Department of Biochemistry,
Wiess School of Natural Sciences, P.O. Box 1892, Houston Texas 77251, U.S.A.
Professor Dirk Reinen, Fachbereich Chemic der Philipps-Universit~t Marburg,
Hans-Meerwein-StraBe, D-3550 Marburg
Professor Peter J. Sadler, Birkbeck College, Department of Chemistry,
University of London, London WCIE 7HX, Great Britain
Professor Raymond Weiss, Institut Le Bcl, Laboratoire de Cristallochimie et de
Chimie Structurale, 4, rue Blaise Pascal, F-67070 Strasbourg Cedex
Professor Robert Joseph P. Williams, Wadham College, Inorganic Chemistry
Laboratory, Oxford OXI 3QIL Great Britain
Table of Contents
Chemical Hardness - An Historical Introduction
R. G. Pearson ......................................
Density Functional Theory of Chemical Hardness
P. K. Chatteraj, R. G. Parr ......................... 11
Hardness and Softness in Density Functional Theory
J. L. G~quez ................................... 27
Hardness Indices for Free and Bonded Atoms
L. Komorowski ................................. 45
The Ground-State Energy of Atomic and Molecular Ions
and its Variation with the Number of Electrons
N. H. March ................................... 71
Isoelectronie Changes in Energy, Electronegativity
and Hardness in Atoms via the Calculations of <r'~>
K. D. Sen ..................................... 87
Charge Capacities and Shell Structures of Atoms
P. Politzer, J. S. Murray, M. E. Grice ................. 101
The Hardness Based Molecular Charge Sensitivities
and Their Use in the Theory of Chemical Reactivity
R. F. Nalewajski ................................ 115
The EEM Approach to Chemical Hardness in Molecules
and Solids: Fundamentals and Applications
B. G. Baekelandt, W. J. Mortier, R. A. Schoonheydt ..... 187
Hardness of Metallic Clusters
J. A. Alonso, L. C. BalbSs ......................... 229
Author Index Volumes 1- 80 ......................... 259
Chemical Hardness- A Historical Introduction
Ralph G. Pearson
Chemistry Department, University of California, Santa Barbara, Ca 93106, USA
A brief account is given of the origin and early development of the idea of hardness, introduced to
chemistry as hard and soft Lewis acids and bases. There is also a discussion of the merging of this
early view of hardness with the modern definition, based on density functional theory.
I Early Work ........................................................... 2
2 Hard and Soft Acids and Bases ............................................ 3
3 The Definition of Hardness ............................................... 7
4 References ............................................................ 10
erutcurtS dna ,gnidnoB .loV 08
~,.(( teV-regnirpS ag nilreB grcblediell 3991
2 Ralph G. Pearson
1 Early Work
The earliest observations leading to the concept of chemical- or absolute-
hardness, go back to the days of Berzelius. It was noted that some metals
occurred in nature as their sulfide ores, and others as their oxide or carbonate
ores. Table 1 puts this in more quantitative terms. Listed are the cohesive
energies, AH ~ for a number of binary metal oxides and sulfides, MX.
MX~ I = M~} + X~AH ~ (1)
It can be seen that the cohesive energies of the oxides are always greater than
those of the sulfides. But the amount, A, by which it is greater for a given metal
can vary greatly. Thus A is as large as 54 kcal mol- 1 for Mg, and as small as
1 kcal mol- 1 for Hg.
If we look at an exchange reaction such as
CaS + CdO = CdS + CaO
AHex = - 16 kcal mol -I (2)
we see that the products are more stable than the reactants. Since CaO would be
converted to CaCO 3 by air, we expect that CdS and CaCO3 are more likely to
be found in nature than CaS and CdCO3, even if CaS were not so readily
hydrolyzed.
The entries in Table 1 enable us to write an order of decreasing A for the
several metals, or rather metal ions.
Mg 2+ > Fe z+ > Ca 2+ > Zn 2+ > pb 2+ > Cu 2+ > Cd 2+ > Hg 2+
This ordering would later bc called an order of decreasing hardness, or increas-
ing softness. To facilitate matters later, the modern symbol 1"1 will be used for
hardness, and 0 for softness. The relationship between them is simply r I = 1/0.
The above ordering presumably is one of decreasing values of rl.
The foundations for the concept of chemical hardness lie in the works of
Schwarzenbach I-1 and Chatt .12,1 Independently, they showed that metal ions
could be divided into two classes, (a) and (b), depending on the relative affinities
for ligands with various donor atoms.
Tabk .1 Cohesive energies of some metal oxides and sulfides at 298K, kcalmol -t
Mg Fe Ca Zn Pb Cu Cd Hg
~H~,MO 932 422 452 471 851 871 841 69
AH~ 581 091 222 341 731 061 231 59
A 45 43 23 72 12 81 61 1
Chemical Hardness - A Historical Introduction 3
class (a) N>> P > As > Sb
O>>S> Se>Te
F>CI>Br>I
class (b) N<<P > As > Sb
O<<S < Se --- Te
F<CI<Br<I
Edwards had done something similar even earlier 13. His classification,
however, depended on the proton basicity and ease of oxidation of various
ligands. He also made the important step of comparing rates of reaction of
various substrates with the same ligands. In 1962, Edwards and I published
a detailed paper on rates of reaction of these substrates (called electrophilic
reagents), with ligands (called nucelophilic reagents). The existence of two
classes of electrophiles was clearly shown.
Metal ions were simply one group of electrophiles. Class (a) metal ions
reacted most rapidly, and more strongly, with nucelophiles which were very
basic to the proton. Class (b) metal ions reacted most rapidly with nucleophiles
that were easily oxidized.
2 Hard and Soft Acids and Bases
The following year I decided to extend what Edwards and I had done for rate
data to equilibrium data. But I soon realized that equilibrium data were too
limited in scope. It was more important, and also easier, to examine the strength
of the bonds formed between different atoms, or groups of atoms.
This was the very heart of chemistry. The way to do this was to adopt the
generalized acid-base view of chemistry introduced by G.N. Lewis I-5.
A + :B~A:B (3)
The Lewis acid, A, may also be called an electron acceptor, or electrophile. The
base, B, is an electron donor, or ligand or nucleophile, depending upon the
context.
Most cations are Lewis acids and most anions are Lewis bases. Therefore
most inorganic compounds, such as CuCI2, are acid-base complexes. The same
is true for complexes ions, such as CuCI 2- . Organic molecules can also be
considered acid-base complexes. For example, CH3OH may be considered the
Lewis acid CH~', combined with OH-. Even free radicals can act as Lewis acids
or bases, using one electron rather than two or zero, as in Eq. (3).
Thus the applications of Eq. 3 cover the entire range of chemistry. Any
general statements that can be made about the strength of the bond in A: B will
be very useful. It was already known that there was no universal order of Lewis
4 Ralph G. Pearson
acid or base strength. Rough orders of acid and base strength were known, but
the obvious rule that strong acids combine with strong bases to form of
strongest bonds was very approximate.
It should also be appreciated that actual experimental data usually did not
refer to reactions like Eq. (3), but instead to exchange reactions, such as
A:B' + A':B ~A':B' + A:B (4)
Hence data on the relative strengths of bonds could also be useful. A typical
example of Eq. (4) would be the formation of a coordination complex in water.
Cu(H20) +2 + CN(HzO)- *-- CuCN § + 2HzO (5)
The solvation of an ion by water is an acid-base reaction, as is the dimerization
of water.
With this view of chemistry in mind, I used a veriety of kinds of experimental
data to classify Lewis acids as being class (a), or class (b). Putting the donor
atoms of various bases in order of increasing electronegativity gives
As<P<Se<S,-~I~C<Br<CI<N<O<F
The criterion used was that class (a) acids formed more stable complexes with
the donor atoms to the right, and class (b) acids preferred donor atoms to the
left. This is essentially the same criterion used by Schwarzenbach and Chatt.
Table 2 shows that results of this initial effort 6. It also shows that I had
decided to rename class (a) and (b) as hard and soft Lewis acids, respectively.
There were two reasons for this change in nomenclature. One was that it was
often useful to use comparative terms for two acids, such as Hg 2+ is softer than
Pb z+. The other came about as a result of thinking about the fundamental
properties of a given acid which made it class (a) or (b). The acceptor atoms of
the first class are usually of high positive charge, small size, and with no
unshared electrons in the valence shell. Class (b) acids have acceptor atoms of
low positive charge, large size and often have unshared pairs of electrons in the
valence shell. These characteristics meant that class (a) acceptor atoms were not
very polarizable, while class (b) acceptor atoms were very polarizable.
Since polarizability means deformation of the electron cloud in an electric
field, and since things that are easily deformed are soft, this led me to call the two
classes of acids hard and soft, respectively. What I really had in mind was
deformation in the presence of other atoms or groups, to which bonding was
occuring. Thus optical polarizability, while a useful measure of softness, was not
quite the correct measure.
Looking at the list of donor atoms for bases given above, it is obvious that
polarizability is high on the left side and diminishes as one goes to the right. By
the same argument as before, bases which donor atoms such as A, P, Se, S or
I were called soft bases. Bases with F, O and N were hard bases. A hard base had
an electron cloud that was difficult to deform chemically. Electrons were held
tightly, so that loss of an electron was difficult, whereas a soft base was easily
deformed, and even oxidized.
Chemical Hardness - A Historical Introduction
Table 2. Classification of Lewis acids
Class (a) or hard Class (b) or soft
H +, Li + , Na + , K + Cu +, Ag + , Au +, TI +, Hg +,
Be z+, Mg 2+,Ca 2+,sr 2+,Sn 2+ Cs +
AI 3+, Se ,+~- Ga 3+, In 3+, La 3+ pd2+, Cd 2+, pt 2+, Hg 2+
Cr 3+, Co 3+, Fe a+, As 3+, Ir 3+ CH3Hg +
Si 4+, Ti a+ ' Zr a+, Th 4+, pu 4+ ' TI ~+, TI(CH3)3, RHa
OV +2 RS +, RSe +, RTe +
UO~+, (CHa)2Sn 2+ t*, Br +, HO +, RO +
BeMe2, BF 3, BCI 3, B(OR)3 12, Br2, INC, etc.
AI(CHa)a, Ga(CH3), 3, In- Trinitrobenzene, etc.
(Ell3)3 Chloranil, quinones, etc.
RPOf, ROPO~ Tetracyanoethylene, etc.
RSO~, ROSO~, 3OS O, CI, Br, ,1 R3C
,~"71 15+ ' CI 7+ M ~ (metal atoms)
C3R § , OCR ,+ CO2, CN + Bulk metals
XH negordyh( gnidnob )selucelom
Borderline
Fc 2 + Co 2 ~, Ni 2 ~ Cu 2 +, Zn 2 +, pb 2 +
B(CH3)3,802, NO +
With this new nomenclature it was possible to make a simple, general
statement: "hard acids prefer to coordinate to hard bases, and soft acids prefer to
coordinate to soft bases." This is the Principle of Hard and Soft Acids and Bases,
or the HSAB Principle.
Note that this Principle is simply a restatement of the experimental evidence
which led to Table 2. It is a condensed statement of a very large amount of
chemical information. As such it might be called a law. But this label seems
pretentious in view of the lack of a quantitative definition of hardness. HSAB is
not a theory, since it does not explain variations in the strength of chemical
bonds.
The data of Table 1 reveal another ambiguity in the statement of the HSAB
Principle. The cohesive energy of all the oxides is larger than that of the sulfides.
What distinguishes the hard Mg 2§ from the soft Hg 2§ is the magnitude of the
difference.
The explanation for the larger values of AH ~ for 0 2- over S 2- is that the
oxide ion is a stronger base, because of its smaller size. Also the much larger
value of AH ~ for MgO compared to HgO, is because the magnesium ion is
a stronger acid than mercuric ion, again because of size. Thus the word "prefer"
in the HSAB Principle refers to some extra stabilization in a hard-hard, or
soft-soft combination. Alternatively, there could be a destabilization in a hard-
soft pair.
Looking back at reaction 4, it illustrates the HSAB Principle in the following
sense:
hs+sh=hh+ss 0>AH (6)
6 Ralph G. Pearson
where h is read as the harder of the two acids (bases) and s as the softer of the
two bases (acids) .1"6 Thus the reaction is exothermic if the acid-base complexes
are matched up hh and ss.
This rule is not inviolate because of the complication due to acid-base
strength. Strength here is used as a catch-all phrase to mean all the other things
that determine bond energies. These include charges and sizes, electronegativity,
matching of orbital overlaps and steric repulsions. For Eq. )6( to be valid, one
must compare acids, or bases, of the same charge, and roughly of the same
strength.
Table 2 lists some acids such as Si 4+ and Th 4§ which have no real existence,
and where the charges refer to oxidation states. The true acids are species such
as (RO)3Si § or SiH~. The hardness of a given center depends strongly on the
attached groups. The general rule is that hard ligands (bases) make the central
atom hard, and soft ligands make the central atom soft. This observation was
first made by Klixbull Jorgensen 6, who named the phenomenon the "sym-
biotic effect."
Si(OR)~" is harder than SiH~, accordingly 7. In Table 2, we see that BF3 is
hard and BH 3 is soft. The explanation for the symbiotic effect is readily seen. In
BF3, the bonding is very ionic and boron has an actual charge close to its
oxidation state of 3 +. In BH3, the bonding is covalent and boron has an actual
charge of close to zero. Increased positive charge on the acceptor atom always
increases the hardness.
Theoretical explanations of the HSAB Principle were also quickly put
forward 5, 8. The most important feature was that hard-hard combinations
were held together by ionic bonds, primarily, and soft-soft combinations used
covalent bonding. In addition, various stabilizing effects of combining two
polarizable species could be postulated.
Solvation energies also played a role, but an indirect one. For example, in the
gas phase F- is always a stronger base than I-, because of size. In aqueous
solution F- has a greater heat of hydration than I- by 53 kcal/mol. This
difference is what enables I- to complete with F- for various Lewis acids in
water. For soft acids, I- wins out. For hard acids F- is still the stronger base.
In spite of these various complications, the HSAB concept proved to be
useful in many applications to chemistry, as well as to chemically related fields,
such as medicine and geology 9. Two of the articles on HSAB 5, 10 have
been identified by Current Contents as among the most widely quoted publica-
tions in the chemical literature.
For many chemists the vague terms "hard" and "soft" seemed to fill a need in
their chemical vocabularies. The very fact that they were ill-defined terms
probably made them more useful. An analogy might be made to the term
"solvent polarity", which is hard to define, but quite indespensable to chemists
running reactions in solution.
For other chemists the words "hard" and "soft" were anathema. Quantities
which could not be measured, and to which numbers could not be assigned,
were held to have no place in exact science. I also think there was a prejudice
