Hard and Soft Acids and Bases, Ralph G. Pearson Northwestern University Evanston, Illinois 60201
HSAB, Part II
Underlying theories It must be emphasized again that the HSAB principle is intended to be phenomenological in nature. This means that there must be underlying theoretical reasons which explain the ehemical 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 acids and bases into two classes, each with its characteristic behavior. Of course a major part of solvent-solute 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-basc eomplexation. The oldest and most obvious explanation may be called the ionic-covalent theory. It goes back to the ideas of Grimm and Sommerfeld for explaining the differences in properties of Agl and NaCl. Hard acids are assumed to bind bases 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 bind bases primarily by covalent bonds. For good covalent bonding, the two bonded atoms should be of similar size and similar electronegativity. For many soft acids ionic bonding would be weak or nonexistent because of the low charge or the absence of charge. It should be pointed out that a very hard center, sueh as I(VII) in periodate or Mn(VII) in M11O4-, 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 7r-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 it 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 discussed the fundamental principles of the law of Hard and Soft Acids and Bases. 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 it bonds 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 ¶- bonds.
Figure 1. A p-atomic orbital on a ligand atom and d orbital on a metal atom suitable for 7r-bonding. The d orbital is filled and the p orbital is empty for a soft acid-soft base combination. The d orbital is empty and the p orbital is filled for a hard acid-hard base combination. The plus and minus signs refer to the mathematical 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 stabilization 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 stability due to London forces will always exist in a complex formed between a polarizable acid and a polarizable base. Iii this way the affinity of soft acids for soft bases can be partly accounted for. Mulliken (22) 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 7r-bonding molecular orbitals and the 7r*-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
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Table 5.
Calculated Softness Character (Empty Frontier Orbital Energy) of Cations and Donors'1 Orbital
Ion Al34 La34
Tii
+
Be24
Mg24
Figure 2. Atomic orbital hybrids for (a) bonding ond jb) antibonding molecular orbitals. These atomic hybrids are formed by combining a 4 p and a 5 d orbital on each bromine atom. The hybrids are then combined to form the molecular orbitals.
CV + Fe3 +
Sri + Cr3 +
Ba! + Ga34 Cr24
Figure 2 shows the appearance of the hybrid orbitals on two bromine atoms. These arc 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. Mulliken's theory is the same as Chatt's ir-bonding theory as far as the ^-bonding orbital is concerned. The new feature is the stabilization due to the antibonding molecular orbital. As Mulliken points out, this effect can be more important than the more usual wbonding. 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 (23) 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*, 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 H+, which turns out to he a borderline case by calculation, but experimentally is very hard. Probably it is a special case because of its small size. TP+ is predicted to be softer than TI+, as is known to be true experi-
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Fe2 +
Li
+
II4 Ni24 Na+ Cu24 T14 Cd24
Cu4 Ag4 Tl34 Au4 Hg24
energy
(eV)
26.04 17.24 39.46 15.98 13.18 10.43 26.97 9.69 27.33 8.80 28.15 13.08 14.11 4.25 10.38 15.00 3.97 15.44 5.08 14.93
6.29 6.23 27.45 7.59 16.67
De-solvation6 energy (eV)
Et„ (eV)
32.05 21.75 43.81 19.73 15.60 12.76
6.01 4.51 4.35 3.75 2.42
2.33. 2.22 2.21
29.19 11.90 29.39 10,69 29.60 13.99 14.80
Hard
2.06 1.89 1.45 0.91 0.69 0.49
4.74 10.8 15.29 3.97 14.99 3.20 12,89 3.99 3.41 24.08 3.24 12.03
0.42) 0.29
Borderline
0
-0.55' -1.88
-2.04 -2.30, 2.82' -3.37 -4.35 4.64 j —
Soft
—
Etn F~ H20
0H~ Cl~ Br“ CNsnIH“
6.96 15.8 5.38 6.02 5.58 6.05 4.73 5.02 3.96
5.22
-12.18
-5.07)'
-(10.73)
5.07 3.92 3.64 2.73 3.86 3.29 3.41
-10.45 -9.94 -9.22 -8.78 -8.59 -8.31 -7.37
Hard
Soft
Klopman (23). Refers to aqueous solution. c This value is negative, as it would be in general for neutral ligands, because the solvation increases rather than decreases during the removal of the first electron. The numerical value has been put equal to the value for OH in absence of more reliable data. •
6
-
The numbers, Ei, consist of two parts: the energies of the frontier orbitals themselves, in an average bonding condition, and the changes in solvation energy that accompany electron transfer, or covalent bond formation. It is the desolvation effect that makes Al3+ 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! In 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 CaF2(g) + Hgl2(g)
—
CaL(g) + HgF2(g)
(19)
is endothermic by about 50 keal. 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 not involve multiplying together Exm and E'n. 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 Exn (hard-hard combination), or for large negative values of Exm with small negative values of Exn (soft-soft combinations). This explains the HSAB principle. It 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 enthalpy change. This is exactly what is observed in aqueous solution (24). The generally good agreement between Klopman’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 xr-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, It has been a great temptation to try to can exist. with some easily identified physical softness equate property, such as ionization potential, redox potential, or polarizability. All of these give roughly the same None is suitable as an order, but not exactly the same. 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
In 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 HF compared to HI. While the explanations will change, the chemical facts will remain. It is these facts that principle deals with. In spite of several efforts, it does not seem possible to write down quantitative definitions of hardness or softness at 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 conflicting in detail, usually conform to the same general pattern. The looseness of meaning in the terms hard and soft does create some pitfalls in the application of the HSAB pi'inciple. 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 tei'm stable is applied to a chemical compound, One must specify whether it is thermodynamic or kinetic stability which is meant, 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. It 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 H». 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. In other cases it is really necessary to compare four compounds, the possible combinations of two Lewis acids with two bases, as in eqn. (2). An example might be 2LiBu(l) + ZnO(s) ^ LijO(s) + ZuBu2(l)
(20)
—17 kcal shows that Zn2 + is softer The value of AH 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 Li+, aixd that O2- is a stronger base than n-C-iHa-. 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. It follows from what was said that the strongest acids are usually hard (not all hal'd acids are strong, however). Many, but not all, soft bases are quite weak (benzene, CO, etc.). One expects, in general, that the strongest bonding will 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. =
A:B' + A':B
A:B + A':B'
(2)
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':B' is necessarily formed as a by-product, even though its bonding may be quite weak. It is in cases where the two acids or the two bases, or both, are of comparable strength that the effect of softThis can be ness or hardness becomes most important. seen from a consideration of eqn. (10). Applied to reaction (2), this leads to the predicted equilibrium constant log K
—
(jSa
—
8a') (Sb
—
-
XA) (A'b
-
A'n)
(29)
where the X’s are the electronegativities. This gives a value of All equal to 46(1.0 +21 0.7) (4.0 2.5) kcal, for reaction (27). Table 6 shows a number of heats of reaction calculated by Pauling’s eqn. (29), compared to the experimental results. It can he seen that the equation is totally unreliable in that it gives the sign of the heat change incorrectly. Many other examples can be chosen, some of which will agree 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 (30). Among the representative and early transition elements, A' 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 will increase relative to that for I. The prediction is also made for preferred bonding to O compared to S, and X compared to P. The facts are always otherwise. Similarly, if one goes across the periodic table, the electronegativity of the elements increases steadily. This leads to the Pauling prediction that in a sequence such as Na, Mg, Al, Si the affinity for I will increase relative to that, for F. Similarly, bonding to S and P atoms will be preferred relative to O and N. However, as long as the elements have the positive group oxidation states, the facts are the opposite 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 the heat of reaction in eqn. (28) if the oxidation state of the bonding atoms change, or if the other groups attached to these atoms Such changes affect the electronegaare changed? tivity in a predictable way. For example, the A’s of Pb(II) and Pb(IV) are 1.87 and 2.33, respectively, (31). Similarly, the A value of carbon is 2.30 in CH3, 2.47 in CH2CI and 3.29 in Cl1/ (32). Increased positive oxida—
This equation equation 6
Dab
=
comes
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 (A = 2.1), and since oxygen (A 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
=
—
from the Pauling (&9) bond energy
VFDaa + Dbb) + 23 (Aa
where Dab is the bond energy of an
—
A+)2
AB bond, etc.
ClhCOOH + I1A
CIbCOA + IbO
(31)
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 arc not due to a poor choice of the A values of the elements. No reasonable adjustment of these values will improve the situation. If new parameters XA, A'B, etc., are found for the elements to give the best lit 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 Tl, Hg, etc.), and as electronegative substituents are put on the bonding atoms A or C. For donor atoms A may be taken as a measure of the hardness of the base, donors of low A 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 heat of reac-
tion. 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
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interesting applications to organic chemistry will appear shortly in papers by Saville (35). 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. It 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. In 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 work described in this paper. Thanks are also due to Professor F. Basolo and to Dr. B. Saville for many helpful discussions.
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Literature Cited (18) Jorgensen, C. K., Structure and Bonding, 1, 234 (1966). (19) Deago, R. S., and Purcell, K. F., Prog. Inorg. Chem., 6, 217 (1965). (20) Chatt, J., Nature, 177, 852 (1956); ChaTt, J., J. Inorg. Nucl. Chem., 8, 515 (1958). (21) Pitzer, K. S., J. Chem. Phys., 23, 1735 (1955). (22) Mulliken, R. S.t J. Am. Chem. Soc., 77, 884 (1955). (23) Klopman, G., J. Am. Chem. Soc., 90, 223 (1968). (24) Ahrland, S., Helv. Chem. Ada, 50, 306 (1967). (25) Hildedrand, J. H., and Scott, R. L., “Solubility of NonElectrolytes,” Dover Publications, Inc., New York, N. Y., 1964.
(26)
Angell,
C. M., 5192 (1966).
and
Gruen, D. M., J. Am.
Chem. Soc., 88,
(27) Basolo, F., and Raymond, K., Inorg. Chem., 5, 949 (1966). (28) Prue, J., “Ionic Equilibria,” Pergamon Press, Oxford, 1965, p. 97. (29) Pauling, L., “The Nature of the Chemical Bond” (3rded.), Cornell University Press, Ithaca, N. Y., 1960, pp. 88-105. (30) Pearson, R. G., Chem. Comm., 2, 65 (1968). (31) Allred, A. L., J. Inorg. Nud. Chem., 16, 215 (1961). (32) Hinze, H. J., Whitehead, M. A., and Jaff£, II. IT., J. Am. Chem. Soc., 85, 148 (1963). (33) Pearson, R. G., and Songstad, J., J. Am. Chem. Soc., 89, 1827 (1967). (34) Hine, J., and Weimar, R. D., J. Am. Chem. Soc., 87, 3387 (1965). (35) Saville, B., Angew. Chem. (International Edition), 6, 928 (1967).
