Hard and Soft Acids and Bases,
Ralph G. Pearson
Northwestern University
Evonston, Illinois 60201
HSAB, Part II
Underlying theories
It must he emphasized again that the
HSAB principle is intended to he phenomenological in
nature. This means that there must he underlying
theoretical reasons which explain the chemical facts
which the principle summarizes. It seems certain that
there will be no one simple theory. To explain the
stability of acid-base complexes, such as A:B, will require a consideration of all the factors which determine
the strength of chemical bonds.
Any explanation must eventually lie in the interactions occurring in A:B itself. Solvation effects, while
important, will not in themselves cause a separation of
Lewis aeids and hases into two classes, each with its
characteristic behavior. Of course a major part of
solventrsolute interaction is itself an acid-base type of
reaction (19). With regard to the bonding in A:B,
several pertinent theories have been put forward by
various workers interested in special aspects of acid-hase
complexation.
The oldest and most obvious explanation may be
called the ionic-covalent theory. I t goes back to the
ideas of Grimm and Sommerfeld for explaining the
differences in properties of AgI and NaC1. Hard acids
are assumed to bind hases primarily by ionic forces.
High positive charge and small size would favor such
ionic bonding. Bases of large negative charge and
small size would be held most tightly-for example,
OH- and F-. Soft acids hind bases primarily by
covalent honds. For good covalent bonding, the two
bonded atoms should he of similar size and similar electronegativity. For many soft acids ionic bonding
would he weak or nonexistent because of the low charge
or the absence of charge. It should be pointed'out that
a very hard center, such as I(VI1) in periodate or R h (VII) in lLlnOa-, will certainly have much covalent
character in its bonds, so that the actual charge is reduced much below +7. Nevertheless, there will be a
strong residual polarity.
The a-bonding theory of Chatt (20) seems particularly appropriate for metal ions, but it can be applied to
many of the other entries in Table 4 as well. According
to Chatt the important feature of class (b) acids is considered to be the presence of loosely held outer d-orbital
electrons which can form a bonds by donation to suitable ligands. Such ligands would be those in which
empty d orbitals are available on the basic atom, such as
The first part of this article appeared on p. 581 of the September issue of THIS JOURNAL
and disccmed the fundmnental
principles of the law of Hard and Soft Acids and Baes. Numbers
of equations, footnotes, and references follow consecutively those
in Part I.
phosphorus, arsenic, sulfur, or iodine. Also, unsaturated ligands such as carbon monoxide and isonitriles
would be able to accept metal electrons by means of
empty, but not too unstable, molecular orbitals. Class
(a) acids would have tightly held outer electrons, but
also there would be empty orbitals available, not too
high in energy, on the metal ion. Basic atoms, such as
oxygen and fluorine in particular, could form s honds in
the opposite sense, by donating electrons from the ligand
to the empty orbitals of the metal. With class (b)
acids, there would be a repulsive interaction between the
two sets of filled orbitals on metal and oxygen and
fluorine ligands. Figure 1 shows schematically a p
orbital on the ligand and a d orbital on the metal atom
which are suitable for forming a honds.
Figure 1. A p-otomic orbital on a
ligond atom and d orbit01 on a
metal atom suitable for r-bonding. The d orbital is filled and
the p orbital is empty for o soft
odd-loft base rombinotion. The
dorbital is empty and theporbitol
is filled for a herd acid-hard
bore combinmtion. The plus and
minus signs refer to the mothemoticol sign of the orbital.
Pitzer (21) has suggested that London, or van der
Waals, dispersion energies between atoms or groups in
the same molecule may lead to an appreciable stahilization of the molecule. Such London forces depend on
the product of the polarizabilities of the interacting
groups and vary inversely with the sixth power of the
distance between them. These forces are large when
both groups are highly polarizable. It seems plausible
to generalize and state that additional stahility due to
London forces will always exist in a complex formed between a polarizable acid and a polarizable base. In this
way the affinity of soft acids for soft bases can be partly
accounted for.
11ulliken ( B )has given a different explanation for the
extra stability of the bonds between large atoms-for
example, two iodine atoms. It is assumed that d-porbital hybridization occurs, so that both the s-bonding
molecular orbitals and the T*-antibonding orbitals contain some admixed d character. This has the two-fold
effect of strengthening the bonding orbital by increasing
overlap and weakening the antibonding orbital by decreasing overlap.
Volume 45, Number 10, October 1968
/
643
Table 5.
Ion
Figure 2. Atomic orbital hybrids for la) bonding and (b) ontibonding
molecular orbitolr These atomic hybrids are farmed by combining a 4 p
and o 5 d orbital on each bromine atom. The hybrids are then combined
to form lhe molewlor orbital%.
Figure 2 shows the appearance of the hybrid orbitals
on two bromine atoms. These are now added and subtracted in the usual way to form bonding and anti-bonding molecular orbitals. The bonding orbital will clearly
have a greater overlap than if it were formed by adding
a p atomic orbital from each bromine atom. Hence it
will be more bonding. The anti-bonding molecular
orbital will overlap less than if it were formed by substracting two p atomic orbitals. Hence it will be less
anti-bonding.
nhlliken's theory is the same as Chatt's r-bonding
theory as far as the r-bonding orbital is concerned.
The new feature is the stabilization due to the antibonding molecular orbital. As Mulliken points out, this
effect can he more important than the more usual Tbonding. The reason is that the antibonding orbital is
more antibonding than the bonding orbital is bonding, if
overlap is included. For soft-soft systems, where there
is considerable mutual penetration of charge clouds, this
amelioration of repulsion due to the Pauli principle
would be great.
Klopman (83) has developed an elegant theory based
on a quantum mechanical perturbation theory. Though
applied initially to chemical reactivity, it can apply
equally well to the stability of compounds. The
method emphasizes the importance of charge and
frontier-controlled effects. The frontier orbitals are
the highest occupied orbitals of the donor atom, or base,
and the lowest empty orbitals of the acceptor atom, or
acid. When the difference in energy of these orbitals is
large, very little electron transfer occurs and a chargecontrolled interaction results. The complex is held
together by ionic forces primarily.
When the frontier orbitals are of similar energy, there
is strong electron transfer from the donor to the acceptor. This is a frontier-controlled interaction, and
the binding forces are primarily covalent. Hard-hard
interactions turn out to be charge-controlled and softsoft interactions are frontier-controlled. By considering ionization potentials, electron affinities, ion sizes, and
hydration energies, Klopman has succeeded in calculating a set of characteristic numbers, E f , for many cations
and anions.
These numbers, Table 5, show an astonishingly good
correlation with the known hard or soft behavior of each
of the ions as a Lewis acid or base. The only exception
is Hf,
which turns out to be a borderline case by calculation, but experimentally is very hard. Probably it is a
special case because of its small size. TI3+is predicted
to be softer than TI+, as is known to be true experimentally.
644
/
Journal of Chemicol Education
Calculated Softness Character (Empty Frontier
Orbital Energy) of Cations and Donors"
Orbitd
energy
(eV)
Desolvationb
energy
AP+
Laa+
Ti'+
Be'+
Mg'+
Ca2+
Fez+
SrP+
CrS+
Bas+
Gas+
Cr2+
FeP +
Li +
H+
Nia+
Na +
cu2+
TI +
Cd4+
Cu'
6.01'
4.51
4.35
3.75
2.42
2.33,
2.22
2.21
2.06
1.89
1.45
0.91
0.69
Hard
.
Borderline
-0.55
-1.88
-2.04
-2.30
-2.82)
-3.37
-4.35
-4.64
8
'.
Au
I
+
Hg'+
FH20
OHC1BrCNSHIH-
EL
(eVI
. .
6.96
15.8
5.38
6.02
5.58
6.05
4.73
5.02
3.96
5.22
(-5.07)'
5.07
3.92
3.64
2.73
3.86
3.29
3.41
1
-1218
~(10.73)
-10.45
-9.94
-9.22
-8.78
-8.59
-8.31
-7.37
}
Soft
Hard
Soft
'KLOPMAN
(83).
LRefersto aqueous solution.
GThisvalue is negative, as it would be in general for neutral
ligands, because the salvation increases rather than decreases
during the removal of the first electron. The numerical value has
been put equal to the value for OH- in absenoe of more reliable
data.
The numbers, E f , consist of two parts: the energies
of the frontier orbitals themselves, in an average bonding condition, and the changes in salvation energy that
accompany electron transfer, or covalent bond formation. It is the desolvation effect that makes Ala+hard,
for example, since it loses much solvation energy on electron transfer. All cations would become softer in less
polar solvents. Extrapolation to the gas phase would,
in fact, seem to make the hardest cations in solution
become the softest! I n the same way, the softest anions
in solution seem to become the hardest in the gas phase.
This suggests that it is not reasonable to extrapolate the
interpretations from solution into the gas.
It should be remembered that much of the data on
which Table 4 (Part I) is based was obtained from
studies in the gas phase, or in solvents of very low
polarity. Thus the characteristic behavior of hard and
soft Lewis acids exists even in the absence of solvation
effects. For example, the reaction
CaFdg)
+ HgL(g) * Cab(g) + HgFdg)
(19)
is endothermic by about 50 kcal. The hard calcium ion
prefers the hard fluoride ion, and the soft mercury ion
prefers the soft iodide ion, just as they would in solution.
When the electron donor and electron acceptor are
brought together (in solution) to form a complex, the
change in energy may be calculated by Klopman's
method. The calculation does s o t involve multiplying
together Exm and EL. Instead their difference becomes important, as well as the magnitude of the exchange integral between the frontier orbitals. This
must be estimated in some way.
The most stable combinations are found for large
positive values of Exm with large negative values of Ef,,
(hard-hard combination), or for large negative values of
Etm with small negative values of Ez,, (soft-soft combinations). This explains the HSAB principle. I t is
also noteworthy that the theory predicts that complexes
formed by hard cations and hard anions exist because
of a favorable entropy term, and in spite of unfavorable
enthalpy change. Complexes of soft cations and anions
exist because of a favorable euthalpy change. This is
exactly what is observed in aqueous solution (84).
The generally good agreement between Rlopman's
approach and the experimental properties of the various
ions does suggest that the simple explanation based on
hard-hard binding being electrostatic and soft-soft
binding being covalent, is a good one. There is no
reason to doubt, however, that r-bonding and electron
correlation in different parts of the molecule can be more
or less important in various cases. The electron correlation would include both London dispersion and Mulliken's hybridization effect.
It is just because so many phenomena can influence
the strength of binding that it is not likely that one scale
of intrinsic acid-base strength, or of hardness-softness,
can exist. It has been a great temptation to try to
equate softness with some easily identified physical
property, such as ionization potential, redox potential,
or polarizability. All of these give roughly the same
order, but not exactly the same. None is suitable as an
exact measure (18). The convenient term micropolarizability may sometimes be used in place of softness
to indicate that deformability of an atom, or group of
atoms, at bonding distances is the important property.
Some Applications of the HSAB Principle
I n conclusion we may say that in the broadest sense
the HSAB principle is to be regarded as an experimental
one. Its use does not depend upon any particular
theory, though several aspects of the theory of bonding
may be applicable. No doubt the future will bring
many changes in our ideas as to why HOI is stable compared to HOF, whereas the reverse is true for H F compared to HI. While the explanations will change, the
chemical facts will remain. I t is these facts that principle deals with.
I n spite of several efforts, it does not seem possible to
write down quantitative definitions of hardness or softness a t this time. Perhaps it is not even desirable, lest
too much flexibility be lost. The situation is somewhat
reminiscent of the use of the terms "electronegativity"
and "solvent polarity." Here also no precise definitions exist or, rather, many workers have established
their own definitions. The several definitions, while
confliating in detail, usually conform to the same general
pattern.
The looseness of meaning in the t e r m hard and soft
does create some pitfalls in the application of the
HSAB principle. Problems do arise particularly in discussing the "stability" of a chemical compound in terms
of the HSAB principle. A great deal of confusion can
result when the term stable is applied to a chemical compound. One must specify whether it is thermodynamic
or kinetic stability which is meaut, stability to heat, to
hydrolysis, etc. The situation is even worse when a
rule such as the principle of hard and soft acids is used.
The rule implies that there is an extra stabilization of
complexes formed from a hard acid and a hard base, or a
soft acid and a soft base. I t is still quite possible for a
compound formed from a hard acid and a soft base to be
more stable than one made from a better matched pair.
All that is needed is that the first acid and base both be
quite strong, say H + and H- combined to form H2.
A safer use of the rule is to use it in a comparative
sense, to say that one compound is more stable than
another. This is really only straightforward if the two
compounds are isomeric. I n other cases it is really
necessary to compare four compounds, the possible
combinations of two Leuis acids with two bases, as in
eqn. (2). An example might be
The value of AH = -17 lccal sho~vsthat Zn2+is softer
than Li+, which is what we would conclude from their
outer electronic structure. Notice also that it is likely
that Zn2+is a stronger acid than T i + , and that 02-is a
stronger base than n-C4H9-. However, the stable
products do not contain the strongest acid combined
with the strongest base.
The point has been made that the intrinsic strength of
an acid or base is of comparable importance to its hardness or softness. Methods were described for estimating the strength of an acid or a base in terms of its size
and charge, etc. I t follows from what was said that the
strongest acids are usually hard (not all hard acids are
strong, however). Many, but not all, soft bases are
quite weak (benzene, CO, etc.). One expects, in general, that the strongest bonding mill be found between
hard acids and hard bases. The strength of the coordinate bond in such cases may range up to hundreds of
kilocalories.
Many combinations of soft acids with soft bases are
held together by very weak bonds, perhaps only several
kilocalories per bond. Examples would be some charge
transfer complexes. With such weak overall bonding,
one wonders why some soft-soft combinations are
formed at all. A partial answer lies in considering eqn.
(2) which, as mentioned before, represents the more
common kind of chemical reaction actually occurring.
The usual rule for a double exchange of the type above is
that the strongest bonding will prevail. Thus if A and
B are the strongest acid and base in the system, reaction
will occur to form A:B. The product A':B1 is necessarily formed as a by-product, even though its bonding
may he quite weak.
It is in cases where the two acids or the two bases, or
both, are of comparable strength that the effect of softness or hardness becomes most important. This can be
seen from a consideration of eqn. (10). Applied to reaction (2), this leads to the predicted equilibrium constant
log K = ( S A - SA') (SF, - S e ' )
+
- c*')
( 0 ~
(US
- on')
(21)
Thus the It- complex is formed in aqueous solution not
Volume 45, Number 10, October 1968
/
645
so much because of the strength of the binding between
I- and I,, but because It and H,O are both weak acids
and I- and H 2 0 are both weak bases. Hence the first
term on the right hand side of eqn. (21) must he small,
and the second term must dominate. This is an alternative way of saying that the soft I- and 1%
are weakly
solvated by water, whereas water molecules solvate each
other well by hydrogen bonding. Both A' and B' in
eqn. (2) are water molecules, in this case.
Solubility may obviously he discussed in terms of
hard-soft interactions. The rule is that hard solutes dissolve in hard solvents and soft solutes dissolve in soft
solvents. This rule is actually a very old one when used
in the form "like things dissolve each other." Hildebrand's rule for solubility is that substances of the same
cohesive energy density (&E,.,/V) are soluble in each
other (25). Hard complexes, composed of hard acids
and bases, have a high cohesive energy density, and
soft complexes have a low cohesive energy density,
as n rule.
Water is a ~ e r hard
y
solvent, both with respect to its
acidic and basic functions. It is the ideal solvent for
hard acids, hard bases and hard complexes. Alkyl substituents, such as in the alcohols, reduce the hardness in
proportion to the size of the alkyl group. Softer solutes
then become soluble. For example oxalate salts are
quite insoluble in methanol. Dithiooxalate salts are
quite soluble. Benzene would be a very soft solvent,
containing only a basic function, however. Aliphatic
hydrocarbons are rather soft complexes, but have no
residual acid or basic properties to help solvate solutes.
The solvation of cations by water is of paramount importance in determining the electromotive series of the
metals. If one examines the series, one finds at the
bottom of the list in reactivity the metals Pt, Hg, Au,
Cu, Ag, Os, Ir, Rh, and Pd. All of these form soft
metal ions in their normal oxidation states. Their softness is responsible for their lack of chemical reactivity in
aqueous environment.
This can be seen by breaking up the process
M(s) - M t ( a q )
-
+ e-
En
(22)
into three hypothetical parts:
M(s)
M(d
the first two of these require energy: the heat of sublimation and the ionization energy, respectively. Only
the third step gives energy back to drive the entire process. If the hydration energy is relatively weak, the
metal will have a low E o value and be unreactive. Soft
metal ions will indeed have a low hydration energy
compared to the energy requirements of the first two
steps.
This suggests that these unreactive metals may be
made reactive by using a different environment: a
softer solvent or mixture of solvents. It is clear that in
a mixed solvent, metal ions of different hardness or softness will sort out the mixture. For example, in very
concentrated solutions of chloride ion in water, hard
ions such as Mg2+and Ca2+will bind to H20, whereas
softer ions such as Ni2+, Cu2+,Zn2+,and Cd2+will bind
to C1- ($6). Adding chloride ions to water should increase the reactivity of soft metals more than the reac646
/
Journal o f Chemical Education
tivity of hard metals.
It is of interest to note that the difference between
the sum of the ionization potentials and the heat of
hydration of an ion forms a series almost exactly like
those of Table 5. The difference in energy must be
divided by n, the number of electrons lost or gained
by the ion to make ions of different charges comparable (Stan Ashland, private communication).
A useful rule is used by inorganic chemists when they
wish to precipitate an ion as an insoluble salt. The rule
is to use a precipitating ion of the same size, shape, and
of opposite, but equal, charge. For example, Cr(NH&3+ is used to precipitate Ni(CN)? (27); PF6is used to precipitate Mo(C0)6+; hut C03'- precipitates Ca?+; SZ- precipitates Ni2+; I- precipitates
Ag+; etc. In the latter cases a good lattice energy
results from the combination of small ions.
The insolubility of the large ions does not result so
much from a good lattice energy, but from the poor solvation of the large ions, which may be regarded as soft,
weak acids and bases. Even when precipitates are not
formed, it is known that. large cations form complexes, or
ion-pairs, with large anions ($8).
Consider the solid-state reaction
LiI(s)
+ CsF(a)
-
LiF(s)
+ CsI(s)
AHo = -33 kcal
(26)
The final combinations of hard Li+ and hard F- combined, as well as soft Cs+ and soft I-, is much more
stable than the mismatched combination of hard and
soft LiI and CsF. However, simple lattice energy considerations show that i t is the high stability of LiF
(solid) which drives the reaction. The weakly bound
CsI is just along for the ride, so to speak.
In addition to solubility of salts, the tendency to form
salt hydrates can he discussed from the HSAB viewpoint. To form a hydrate, we generally need a cation
or an anion which is hard, so that it has an affinity for
HzO. However, if both the cation and anion are hard,
the lattice energy will be too great and a hydrate will not
form.
The alkali halides provide a nice example. We find
the greatest tendency to form hydrates with LiI, and
least with LiF, which is rather insoluble, in fact. At the
other end, we find that CsF is one of the few simple
cesium salts which does form a hydrate, whereas CsI
does not. I n the latter case, both ions are soft and,
even though the lattice is weak, water has no tendency
to enter.
The simple chemical reaction in eqn. (26) is an extremely informative one. Let us examine it in another way, by converting to the gas phase.
LiI(g)
+ CsF(g)
-
LiF(g)
+ CsI(g)
(27)
I n this case the heat of the reaction is - 17 kcal, so it is
still strongly favored to go to the right as shown.
Again the strong bond between Li and F is decisive.
This is of interest because Pauling ($9)has a celebrated
rule for predicting the hcats of reactions such as in eqn.
(27). According to this rule, a reaction is exothermic if
the products contain the most electronegative element
combined with the least electronegative element.
Since Cs is more electronegat,ive than Li, this rule p r o
dicts that reaction (27) will be endothermic!
Pauling's rule is supposed to be a quantit,at,ive one."
"owever, it is not considered to be quite as reliable for bonds
between two atoms of greatly different electrol~egativities.
Toble 6.
Heotr of Gas Phore Reactions at 25'C
AH......-.
+
+
++
+
++
-48 kcal
-94
+
-2.5
- 10
BeI,
SrF1 = BeF,
SrI,
3NaF = AIF,
3NaI
A14
HI
NaF = HF
N d
HI
AgCI = HCl f AgI
NO1
CuF = CuI
NOF
a
+
-32
AH..,.
a
+35 keal
+I27
+76
+5
+76
Calculated from eqn. (29)
For a rearhion (where A and C are the more metallic elements)
t,he heat of reaction in lical/mole becomes6
AH = 46(Xr - X A )(XB
- Xn)
(20)
where the X's are the electronegativities. This gives a
value of AH equal to 4G(1.0 - 0.7) (4.0 - 2.5) = f 2 1
kcal, for reaction (27).
Table G shows a number of heats of reaction calculated by I'auling's eqn. (29), compared t.o the experimental results. I t can be seen that the equation i:;
totally unreliable in that it gives the sign of the heat
change incorrectly. Many other examples can be
chosen, some of which \\-illagree with eqn. (29) and some
of which will not, as to the sign of AH. However, it is
easy to tell in advance when the equation will fail (SO).
Among t,he representative and early transition elements, X always decreases as one goes down a column in
the periodic table. This leads to the Pauling prediction
that for heavier elements in a column, the affinity for F
mill increase relative to that for I. The prediction is
also made for preferred bonding to 0 compared to S, and
N compared to 1'. The facts are always otherwise.
Similarly, if one goes across t,he periodic table, the
electronegativit,y of the elements increases steadily.
This leads to t,he I'auling prediction that in a sequence
such as Na, Alg, Al, Si t,heaffinity for I will iucrease relative to that for F. Similarly, bonding to S and P atoms
will be preferred relat,ive t,o 0 and N. However, as long
as the element,^ have the positive gronp oxidation states,
the facts are the opposit.e with very few exceptions.
Even more serious, eqn. (29) will almost always predict incorrectly the effect of systematic changes in A and
C. For example, what happens to t,be heat of reaction
in eqn. (28) if the oxidation st,at,eof the bonding atoms
change, or if the other groups attached to these atoms
are changed? Such changes affect the electronegativity in a predictable wag. For example, the X's of
I'b(I1) and l'b(1V) are 1.87 and 2.33, respectively, (51).
Similarly, t,he X value of carbon is 2.30 in CH3, 2.47 in
CHICl and 3.29 in CF3 (52). Increased positive oxidu,'This equation comes from the Pading ($9)bond energy
equation
+
+ 23 ( S A- X B ) ~
DAB= ' / ~ D A ADBB)
where DABis the bond energy of an AR baud, etc.
tion state and substitution of less electronegative atoms
by more electronegative atoms always increases X of the
central bonding atom. From eqn. (29), such changes
again are predicted to decrease the relative affinity for
F, 0, and N, compared to I, S, and P. For all of the
elements, except a few of the heavy post-transition elements (Hg, TI, etc.), the reverse is true.
If organic chemistry is considered in terms of the
HSAB concept, it becomes clear that a simple alkyl
carbonium ion is a much softer Lewis acid than the proton (33). I n an equilibrium such as
the equilibrium constant will be large when A- is a base
in which the donor atom is soft, such as C, P, I, S.
Since carbon is more electronegative than hydrogen (X
= 2.1), and since oxygen (X = 3.5) is more electronegative than any of the soft donor atoms, this could be explained by the use of eqn. (29), which works in this case
(34).
However eqn. (29) predicts that if carbon becomes
more electronegative than carbon in a methyl group, it
will have an even greater affinity for soft donor atoms of
low electronegativity. This is exactly the reverse of
what is found. The more electronegative a carbon
atom becomes, the less it wants to bind to soft atoms.
Certainly the carbon of an acetyl cation is more electronegative than that of a methyl cation. Yet in the reactions
we now find that the equilibrium constant is small if A
has C, P, I, S, etc., as a donor atom.
The poor results of Table 6 are not due t o a poor
choice of the X values of the elements. No reasonable
adjustment of these values will improve the situation.
If new parameters XA, XB, etc., are found for the elements to give the best fit to eqn. (28), they will no
longer be identifiable as electronegativities. They
would necessarily vary with position in the periodic
table, with oxidation state, and with substitution effects
in a way directly opposite from what one would expect
of simple electronegativities.
The Principle of Hard and Soft Acids and Bases may
be used to predict the sign of AH for reactions such as in
eqn. (28). The Principle may be recast to state that, to
be exothermic, the hardest Lewis acid, A or C, will coordinate to the hardest Lewis base, B or D. The softest
acid will coordinate to the softest base. Softness of an
acceptor increases on going down a column in the periodic table; hardness increases on going across the table,
for the group oxidation state; hardness increases with
increasing oxidation state (except TI, Hg, etc.), and as
electronegative substituents are put on the bonding
atoms A or C. For donor atoms X may be taken as a
measure of the hardness of the base, donors of low X
being soft. Accordingly, the HSAB Principle will correctly predict heats of reaction where the electronegativity concept fails. Some exceptions will occur since it
is unlikely that any single parameter assigned to A, B,
C, and D will always suffice to estimate the beat of reaction.
It was not the purpose of this paper to discuss many
applications of the HSAB principle. This has been
done in previous papers ( 1 , 33). A number of further
Volume 45, Number 10, October 1968
/
647
interesting appli~at~ions
to organic chemistry will appear
shortly in papers by Saville (55). One could go on giving examples of the HSAB principle almost without
limit, since they may be picked from any area of chemistry. It is to keep this generality of application that
we have purposely avoided a commitment to any quantitative statement of the principle, or any special theoretical interpretation.
Whatever the explanations, it appears that the principle of Hard and Soft Acids and Bases does describe a
wide range of chemical phenomena in a qualitative way,
if not quantitative. I t has usefulness in helping to
correlate and remember large amounts of data, and it
has useful predictive power. It is not infallible, since
many apparent discrepancies and exceptions exist.
These exceptions usually are an indication that some
special factor exists in these examples. I n such cases
the principle can still be of value by calling attention to
the need for further consideration.
Acknowledgment
The author wishes to thank the U. S. Atomic Energy
Commission for generous support of the \vork described
in this paper. Thanks are also due to Professor F.
Basolo and to Dr. B. Saville for many helpful discussions.
648
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Journol o f Chemical Educofion
literature Cited
(18) JORGENSEN,
C. K., Slruclure and Bonding, 1, 234 (1966).
K. F., Pmg. Inorg. Chem., 6,
(19) DRAW,R. s . , A N D PURCELL,
217 11965).
,
,
(20) CHAET,J., Nature, 177, 852 (1956); Cnnm, J., J. Inmg.
Nucl. Chem., 8, 515 (1958).
K. S., J. Chem. Php., 23, 1735 (1955).
(21) PITZER,
R. S., J. Am. Chem. Soc., 77, 884 (1955).
(22) MUI~LIKEN,
G., J . Am. Chem. Soc., 90, 223 (1968).
(23) KLOPMAN,
S., Helv. Chem. Ada, 50, 306 (1967).
(24) AHRLAND,
J. H.. AND SCOTT.R. L.. '?iolnbilitv of Non(2.5) HILDEBRAND.
, Y.,
~ l e c t r o l ~ t &~) & e r~ublicrthns,I&., New ~ & k N.
1064~
(26) ANRELL,
C. M., AND GRUEN,D. M., J . Am. Chem. Soc., 88,
5192 (1966).
(27) BASOLO,
P.,AND RAYMOND,
K., Inorg. Chem., 5, 949 (1966).
Press, Oxford,
(28)
. . PRUE.
. J.,. '(Ionic Eauilibria,'' Peraarnon
1965,p. 97.
(29) PAULING,
L., "The Nature of the Chemical Bond" (3rd ed.),
Cornell University Press, Ithaca, N. Y.,1960,pp. 88-105.
R. G., Chem. Comm., 2 , 65 (1968).
(30) PEARSON,
A. L., J. Inorg. N d . Chem., 16, 215 (1961).
(31) ALLRED,
(32) HINZE,H. J., WHITEHEAD,
M. A,, AND J A F F H.
~ , H., J. Am.
Chem. Soc., 85, 148 (1963).
R. G., AND SONGSTAD,
J., J. Am. Chem. Soe., 89,
(33) PEARSON,
1827 (1967).
R. D., J. Am. Chem. Soc., 87, 3387
(34) HINE,J., AND WEIMAR,
(1965).
(35) SAVILLE,
B., Angew. Chem. (International Edition), 6 , 928
(1967).