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
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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
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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
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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.
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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).
