Recent advances in the concept of hard and soft acids and bases

Jul 1, 1987 - Recent advances in the concept of hard and soft acids and bases ... The hard / soft acids / bases principle has been justifiably critici...
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Recent Advances in the Concept of Hard and Soft Acids and Bases Ralph G. Pearson University of California, Santa Barbara, CA 93106 Hard and soft acids and hases were originally defined only in general terms ( I ) : soft base-donor atom is of high polarizability, low electronegativity, easily oxidized and associated with empty, low-lying orbitals. hard base donor nram is of low polarirsbility, high electronegati+, hard t u reduce, and associated with emptv orbitals of high energy and hence inaccessible. suit acid* the nceepror atom is of lux positive charge, large R ~ Z P , and has several easily ercired outer electrune. Pularinahle. hard acids-acceptor atom is of high positive charge, small size, and does not have easily excited outer electrons. Not polarizable. Such a qualitative description does not allow for quantification of the property of hardness (or softness, which is simply the inverse of hardness). Thus acids and bases were put into one of two boxes, labeled hard and soft, without any rank ordering. I t was still possible to summarize a great deal of diverse information bv the HSAB Princiole: hard acids orefer to coordinate to hard h a s w and soft acids to soft hases. The statrment refers to the geueralized acid-base reartion A

+ :B

~f

A:B

(1)

While the HSAB Principle has proved useful in many ways (21, it has been justifiably criticized because of the lack of a precise definition of hardness and the inability to assign numbers to the property. Fortunately some recent developments have overcome the above objections. This was done originally by the use of density functional theory, hut the final results are simple and easy to understand. R. G. Parr pioneered the application of density functional theory to chemistry (3). Figure 1 shows a plot of the total electronic energy of a chemical species as a function of the number of electrons, N . The system may he an atom, an ion, a molecule, or a radical. The energiesare all negative, with zero energy way up on top. Experimentally we only know points on the curve for integral values of N, from data such as ionization potentials, I, and electron affinities, A. However, it is convenient to consider that a smooth curve connects the points. In a molecule i t is natural to think of the individual atoms as having nonintegral electron populations. Parr showed that the slope of such a continuous curve is equal to the electronic chemical potential, +.

This property measures the escaping tendency of the electrons in the soecies. It is constant evervwhere within the molecule. If we bring together two chemical species, such as A and B in reaction 1,then electrons will flow from B to A to form a coordinate, covalent hond. But this can only happen if PB is greater than PA (more positive). Furthermore, electron flow will increase PA and decrease p e until they are equal to each other and to the electronic chemical potential of the mole-

Figure 1. Plot of electronic energy vs. number of electrons for a fixed collection of nuclei.

We do not know the instantaneous slope of the curve in Figure 1. However, if we pick the neutral species (or any other) as our starting point, we do know the mean slope for the change from ( N - 1)to N electrons. I t is simply equal to -I. Also the mean slope from N to ( N 1)electrons is simply -A. Using the method of finite differences, we can approximate the slope at N as (I A)/2. But this quantity is simply the Mulliken electronegativity, XM (4).

+

+

Because of this fundamental relation, XM may reasonably he called the absolute electronegativity (3).This name may he unfortunate because XM is now rather different from the original definition of electronegativity as given by Pauling (5)-"the power of an atom in amolecule to attract electrons to itself'. As already mentioned, XM applies to the whole svstem. which mav be an atom. a molecule, an ion, or a radical: The chief use of the Pauling, and similar, scales of electronegativity is to estimate the polarity of each chemical bond and the net charge on each atom in a molecule. I t does this very successfully, and such scales are undoubtedly very useful. However xM adds a new way of looking a t the same problem. For example, consider a molecule X-Y, consisting of two atoms or radicals held together by a hond. The polaritv of the hond determines whether the molecule behaves as x+,Y- or X-, Y + . The same auestion can be asked hv lookine a t the reac-

The difference in energy between the products on the right and those on the left is easily found.

Volume 64

Number 7 July 1987

561

If X has a greater ahsolute electronegativity than Y, AE is positive. This means that X-Y acts as X-, Y+. The answer is a thermodvnamic one and involves no assumntions. While the exampie is in the gas phase, the same resultwould usualIv be found in solution. The sum of the solvation energies of X-and Y+ would be very nearly equal to the sum for X+ and Y-, except when X or Y is the hydrogen atom. When X and Y are brought together, electrons will flow from Y to X, if > X; This lowers xi and raises xy until at equilibrium xx = xy = xxy. This is the electronegativity equalization principle, first proposed by Sanderson as an assumption (6). In density functional theory, it is provahle, provided eq 3 is valid. Absolute Hardness Returning to Figure 1, the next property of the smooth curve that may be of importance is the curvature or rate of change of the slope. For reasons that will become clear, the curvature is used to define 7,the absolute hardness (7).

From the method of finite differences, the operational definition of hardness becomes 7=

(I-A) 2

(5)

We now have an exact definition of hardness, eq 4, and a working definition, eq 5, which can he used to assign numerical values to various chemical species. Note that the units of r, are the same as those of X, namely electronvolts (eV). The nonchemical definition of "hardness" is resistance to deformation or change. Equation 4 shows that hardness is the resistance of the chemical potential to change in the number of electrons. For isolated reactants A and B we can write

A nositive value for the difference means that it costs less energy to transfer an electron from D to C than the reverse. Henre C is rhe Lewis acid and the direction of electron flow is indeed determined by the difference in absolute electronezativities. The magnitude of the difference is an a priori &\,ing potential f(;r the transfer. The above remarks, and eq 8,apply to the net transfer of electrms fn,m D to C. Hut in most cases there will be some elec~rontransfer in both directions. A familiar case is that of ~r back-bonding arcompanving o bonding. For example, 12 is a 1.rwis wid with respect to benzene. There is electron donation from filled a orbitals of benzene tc~the emotv . . o' orbital of iodine. But there is also induced electron transfer from filled a* orbitals of 1 2 to empty a* orbitals of henzene (10). Suppose the amount of electron transfer in both directions is nearlv the same. Then the total energy .. cost is ~ .i v e n by the sum (Ic- A,)

+ (ID- A,)

= 2(1,

+1 ~ )

(11)

Thus hard molecules, where qA and 7~ are both large, resist transfer of electrons in hoth directions. But soft molecules fawr such a cooperative effect. Equation 8 also shows that a net transfer ofelectrons is t'a\,orable fur soft molecules where VA and 7~ are both small. We begin to see the underlying causes of the HSABPrinciple. Soft acids like soft bases because electrons can he transferred readily. Such transfer of electrons, either in one or hoth directions. is necessarv if covalent bondine is to occur. Hard acids will'like hard bases because neithercan transfer electrons readilv. However. thev can still form strone chemical bonds if suitable electr&tacic forces are presentill). Some Experlmental Results While this is encouraging, there is a much more stringent test to be applied to eqs 4 and 5. Many molecules and ions have already been labeled as hard or soft as a result of their chemical behavior. Thus AP+ is a hardLewis acid andTP+ is a soft Lewis acid. Since I and A are known for these species, will the definition q = (I- A)/2 really show this difference? Note that I and A in these cases refer to the processes

where AN is the (fractional number of electrons transferred from B to A upon reaction. Applying electronegativity = ~ gwe , find that equalization,

The difference in electronegativity drives the electron transfer, and the sum of the hardness parameters inhibits electron transfer. While eq 8 seems very reasonable, it is obviously incomplete, because eqs 6 and 7 are incomplete. The chemical potential is a function of the electric potential within the molecule. Initial charges on A or B will affect p~ and PA, as well as the changes in charge due to AN (8).Also there is no allowance made for the energy lowering due to delocalization of the electron density, that is, covalency (9). Nevertheless, eq 8 has its uses, as will be illustrated. I t has the great virtue of using only independently measured properties of the individual reactants to predict how they will interact. Since a Lewis acid is an electron acceptor, it is clear that A should be an important property, but why should I also appear? Similarly for an electron donor, or base, why should A, as well as I, define the reactivity? One reason for this can be seen rather easily. Suppose we pick two new reagents, C and D, instead of A and B in eq 1. C + D e C:D

(9)

T o decide which of the molecules is the acid and which is the base, we must look a t the difference

562

Journal of Chemical Education

Table 1gives a number of values of x" and r, calculated for metal ions. We find that APf is indeed much harder than TP+. All of these cations, and others, give the right results in that the value of 7 agrees with their chemical behavior. The large values of x0 show that these cations will be electron acceptors (acids) and not donors (bases). One mieht well auestion whether the fourth ionization potential of the aluminum arum bas anything to do with its chemical behavior since it is so larre (120 eVI and not for a \.dence shell electron. But it is jusr'this large value that tells us two thing3of importance: hl" will heanelectronacceptor Table 1. Parameters for Some Cations Ion

u".eV

n.eV

only, because x0 is large, and will form ionic honds, rather than covalent, because x" is large. For T13' we can expect more covalent character in the honds that it forms and even some tendency to a hack-bonding. Table 2 gives values of x0 and 7 for a number of neutral molecules and atoms. Note that some negative values of A have hven used. New resnlts have recently ben~meavailable b\, an electron scatterina n~ethoddue ro Srhulr ( 1 2 ) .Enerev &st he added to the chon to make it attach itself to the molecule. The electron is in an unstable antihonding orhital for molecules with negative A values. Though the data is still limited, the results for 7 seem to he about as expected. Hard acids such as BF,, HC1, and Hz0 have large values, though that for SO3 seems too small. Soft acids such as I,. CL. and P t have small values. For related molecules we fixd i f o r R20 > R2S; NR3 > PR3 > AsR3; RCI > RI. Also RC1> RqS > RqP: " . Rq0 - > RqN > CeHa. " - C9Ha. - . The large values of 7 for Hz, Nz, and CO are surprising hut, as we shall see, are consistent with the low reactivity of these molecules. The values of xo are quite interesting. The molecules are arranged in decreasing order of xo, so that Lewis acids should he found in the left-hand column, and hases should be on the right-hand side. In principle, any molecule is an electron donor to all molecules above it in the list. These predictions are borne out remarkably well, hut only if we examine the electron transfer process in more detail. The chemical potential and the hardness are molecular properties and not orhital properties. However, to consider the transfer of electrons from B to A, it is necessary to have the electrons come from a definite occupied orhital in B and to go into a definite empty orhital in A. This defines the relative orientation of A and B to give the greatest possible overlap between these frontier orbitals (13).A major driving force is the formation of a new covalent hond between A and

.

R,.

Sometimes the empty orhital of A is such that a new bond w n he formed without destroying the already existing honds Table 2. Parameters for Some Neutral Molecules Molecule SF$ BF3

so3 Nz Cln SO2 H2 02

PFI GO 12

Fl CHSI HCI CrW CIH+ HsS C6He PHs H2OS CH&I V NH3* lCHd3AS (CHM (CHM (CHd& (CHM

x0.eV

v.eV

7.9 7.8 7.2 7.0 7.0 6.7 6.7 6.3 5.7 6.1 6.0 5.6 4.8 4.7 4.4 4.4 4.3 4.0 4.0 3.1 3.8 3.6 2.9 2.8 2.8 2.7 2.0

7.4 7.8 5.5 8.6 4.6 5.6 8.7 5.9 6.7 7.9 3.4 3.5 4.7 6.0 5.0 6.1 6.4 5.2 6.0 9.5 7.5 3.1 7.9 5.5 5.9 6.0 8.0 6.3

1.5

of the reactants. An example would he the reaction of BF3 with NH3 t o form a stable adduct. Sometimes the empty orhital is strongly antihonding, so that the new bond is formed a t the exuense of an old one. An examole would he NH3 reacting with CH31. If the old hond is a strong one, no electron transfer will take place unless additional activation energy is supplied. That is why SF6. in spite of its large value of xo, will not react with any of the hases in Tahle 2, except under extreme conditions. The large value of x0 for HZis a t first surprising. But i t is in fact quite reasonable, if we remember that hydrogen is a nonmetallic element like oxygen and chlorine. When Hz acts as an electron acceptor, theelectrons go into the a* orbital, causing Hp to dissociate. Only molecules which can form bonds to both hvdroeen atoms can easilv donate electrons to , Hz.A t)piral example is a transition metal atom, where the a d d i t i o ~of~ H . is auite vrooerlv called oxidative addition. The bonding oi C O - t o a transition metal has been the subiect of many theoretical studies. in an attempt to assess the-relative inlportance uf o honding and a hack-bonding ( 1 1 ) . We see from Tahle 2 that in such reactions CO acts as the Lewis acid, and the metal ntom is the Lewis base. Therefore n honding i j more important than n honding. T o form good hands u8ewant transition metal ntomi of low elertn). negativity, surh as \', Fe, or Xi. hfetals such as Pr and Au are LOUelertronegative to be good dwwrs ro C'O. It has heen found that a modificationofeq s c a n he used to estimate the metal-CO hond streneth I l 4 ) . A laree value of ANleads to a stronger hond. In spge of the lack of rigorous iustification for ea 8. it often seems to work. The reason is that both x0 and ?appear in the right places. A small sum for (?A + VB)is favorable for combined a and bonding, as already mentioned. A large difference in x~ and xB will provide greater total bonding, -. the so-called "ionic resonance knergy9*(9). While CO isaLewisacid toward transition metals, itis not an acid toward other hases in Tahle 2, such as NH3. The reason is poor orbital overlap. Ammonia is a a donor, and CO works most efficiently as a n acceptor. Iodine will act as an acid to all the molecules on the righthand side of Tahle 2, toformcharge-transfer complexes. The strength of the hond formed to any base depends both on x, and na. Thus, while H 9 0 has a suitahlv low value of y o . it is too hard to transfer efectron density;and the hond'to'12 is verv weak. Ammonia forms a stroneer hond. and (CH-hN a " . much stronger hond. Using eq 8, we can calculate AN for several hases from Tahle 2 and compare the values with those of the hond dissociation energies. The latter are for the 12-base complexes in nonpolar solvents (15).

..

base

AN

D (kcallmol)

A correlation only exists for very similar molecules. The weak honding for benzene is a result of poor overlap between the orbitals, the n cloud for C6Hs being diffuse. Pyridine, however, which uses the a lone pair on nitrogen, forms an unusually strong bond, with good overlap. Relatlon to MO Theory Molecular orhital theory has proved to be a powerful and versatile tool for both organic and inorganic chemists. I t is almost universally used to explain structure and honding, visible-UV absorption spectra, and detailed mechanisms of chemical reactions. It would he unfortunate if the concepts Volume 64 Number 7 July 1987

563

of absolute electronegativity and hardness conflicted with MO theory or pretended to supplant it. However, they turn out not onlv to be comnatible hut also to be comnlementarv in a useful way. According to MO theory the ionization potential of a molecule is simply the orbital energy of the HOMO, and the electron affinitv is the oribital e n e r n of the LUMO, with changes in sign.

.St --i;-

---

&

i"

-10

These are consequences of Koopmans' theorem. The HOMO is assumed to he doubly occupied. If we make the usual diagram of the molecular orbitals of a chemical system as a function of their energies, we can easily insert x0 and q into the same diagram. An example is shown in Figure 2a. The ionization potential is assumed to be 10 eV, and the electron affinity -1 eV. Then x0 is 4.5 eV, and q is 5.5 eV. The former is shown as a horizontal dashed line on the diagram. It is just the average energy of the HOMO and LUMO, withchange in sign. Clearly it is a good measure of the ability of the molecule toattract electrons to itself. The dashed line is also equal to p, the electronic chemical potential. The hardness is shown as a vertical dashed line. The gap between the HOMO and the LUMO is equal to twice the value of n. This gives a new insight into the meaning of hardness A d sof&ess. A hard moikcule (or ion) has a large aaD between the HOMO and LUMO, and a soft molecule (or ion) has a small gap! For atoms or radicals where the HOMO is only singly occupied (SOMO), the situation is different since the electron affinity usually refers to adding a second electron to the SOMO. In molecular orhital theorv" -u" . is now the averaee " energy of the two electrons in the orbital. And ( I - A) turns out to be just the average value of the interaction energy of the two electrons (16). Figure 2b shows -xo and q for the radical case. Returning to the more interesting case of Figure 2a, the definition that a soft molecule has a small enerw -.-gap, . . and a hard molecule a large energy gap, is completely consistent with the qualitative definitions given in the opening paragraphs of this article. Soft acids and bases have properties that guarantee that the HOMO is relatively high in energy and that the LUMO is relatively low. Hard acids and bases have the opposite properties. The quantum theory of polarizability shows that, in the presence of an electric field, excited states of a system are mixed in with the ground state in such a way as t o lower the energy. The smaller the excitation energy, the greater the effect. A small enerw eao. (I . - A). means that a whole manifold of excited states lies near the ground state. Thus a small eaD means hieh ~olarizabilitv.and soft acids and bases will heeasily polarGed. However, the excited states involved in polarization are not exactly the same as those involved in chemistry. Optical polarizabilities are similar to, but not the same, as chemical polarizability (171. The energy gap between HOMO and LUMO usually defines the lowest energy electronic absorption hand. Soft acids and bases should absorb light closer to the visible than hard acids and bases. H20, H2S, H2Se, and H2Te have their first absorption maxima a t 1655, 1950, 1970, and 2000 A, respectively. In organic chemistry chromophoric groups are unsaturated ones, like uu

These groups always correspond to relatively high energy HOMO'S, and low energy LUMO's. We can see the basis for the rule that unsaturation increases softness. 564

Journal of Chemical Education

t

LUMO

I

-'

HOMO

SOMO

Figure 2. Orbital energy diagrams showing ,yo and 7 f w (a) filled-shell molecule, and (b) atom or radical.

L-M-L Fogure 3 Orbital energy aiagrarns far frontier orbitals of a mo a c ~ l sML?, . in the olable ( lnearr form, and an mstaole (bent) form See Z eg er. T horg Chem l985,24, 1547.

I t would be verv convenient if it were ~ossibleto evaluate ( I - A) from measured vis-UV spectra. However, this is not easv to do. For exam~le.Nhv = 7.5 eV for the absorotion band of water quoted above, but (I - A) = 19.0 eVfrom Table 2. There are two reasons for the discrepancy. One is that adding an electron to form HzO- would produce a much larger change in interelectronic repulsion than does the simple promotion of an electron from the HOMO to the LUMO. This increases ( I - A) by a very substantial amount. The second reason is even more serious. In addition to the antibonding MO's, which include the LUMO, there are also empty orbitals, which are essentially atomic orbitals heyond the valence shells. These give rise to the so-called Rydberg transitions in the UV. I t is m i t e nossible that a Rvdbere MO state is lower in energy than t'hr ~ 6 ~ 0 - L Utransition: In the rase of HvO it is believed that the first L'V band is. in fact, partly a idb berg transition to the 3s orbital of oxygen (18). Another consequence of a small energy gap is enhanced chemical reactivity in general. Consider a unimolecular reaction first, such as-a dissociation into smaller fragments, or rearrangement of an unstable isomer to a more stable one. Quantum mechanically this also happens by mixing excited state wave functions of the reactant molecule in with the

hard

soft

Figure

4. Partial bansfer of electrons from HOMO's of each molecule to LUMO's 01 the other (delocaliration),and mixing ol excited orbitals within the same molecule (polarization).

ground state wave function. The ease of mixing again depends inversely on the promotion energy. A small HOMOLUMO gap means that reaction can occur more readily. We can conclude that soft molecules are more reactive than hard molecules, in unimolecular reactions. Thus the order of decreasing thermal stability would be H z 0 > H2S > H2Se > H2Te. This way of looking a t reactivity is called the second-order Jahn-Teller effect (19). Suppose we have a complex, such as Pd(P(CH3)&, that could exist in either a linear or a hent form. Quantum mechanical calculations would show a much larger HOMOLUMO gap for the stable structure (linear) than for the unstable (hent) form. This is shown in Figure 3. There seems to he a rule of nature that molecules arrange themselves so as to he as hard as possible. A large HOMO-LUMO gap increases stability. Soft molecules will also be more reactive than hard molecules in bimolecular reactions, providing partial electron transfers are reauired. This follows from the use of nerturbation theory for chemical reactions, pioneered by ~ k w a (20) r and Fukui (21). Figure 4 shows the MO diagrams of two interacting molecules, R and S. The two are of similar electronegativities, so electron transfer will occur in hoth directions. One molecule, however, ismuch harder than the other. Two kinds of interactions are shown: 1. Partial transfer of electrons from the HOMO of each molecule to

the LUMO of the other. This wcurs by mixing of the orbitals. 2. There is a mixing of the filled MO's of each molecule with its own empty MO's.

The first effect is called delocalization and is the mechanism whereby new bonds are formed between the reactants and old bonds are broken. Other orbitals hesides the HOMO's and LUMO's mav be involved to a lesser extent. The second effkct is called polarization. I t has the effect of lowering the repulsive energy between the two molecules as they approach each other. Polarization is easiest when the energy gap is small for each molecule. Considering only the four frontier orbitals, an approximate value for the energy lowering due to delocalization is given by

The 6's are exchanee intemals of the perturbation Hamiltonian over the interacting MO's.One icould correspond to a bonding, and the other t o r bonding, for example. The stahilization is greatest if A is large for hoth molecules and I is

small. This means that both energy gaps should he small or hoth molecules should be soft. The second effect is closely related to the optical polarizability discussed earlier. A soft acid and a soft base will interact favorably with each other as a result of mutual polarization. We see another ex~lanationfor the Princinle of Hard and Soft Acids and ~ a s e emerging i from this discussion. A third effect in the interaction of two molecules is not shown in Figure 4. This is the electrostatic effect, due to charges and dipoles on the reactants. Hard acids and bases must rely on this type of bonding. We can now give another qualitative definition of what is meant by chemical hardness, 7. A hard molecule resists changes in its electronic charge cloud. Not only are changes in the total amount of charge resisted, but changes in the charge distribution in space are resisted. A soft molecule has an easily changed electron distribution. Are Anlons Son7 So far we have not presented a table of x and 7 values for anions. There is a big experimental difficultv in this case: i t is unlikely that we will be able to measure el'ctron affinities, to form Br2-, for example.' For closed shell anions, such as Br-, we can be sure that A would be a large negative number because the added electron is in a higher orbital than the valence shell and because of large interelectronic repulsions. Since the ionization potentials of anions are small, it would a m e a r that y o for most anions will he a neeative number;&responding to a positive value of p. This isquite reasonable; the escaping tendency of electrons in Br2- would be indeed large. Also the value of 7 would be quite large. This is disconcertine, .since we would expect Br2-to he vervnolar". izable, or soft. This hypothetical hardness of anions is due entirely to their resistance to the addition of electrons, to the large negative A values. In a similar way, the large values of 7 for cations (Table 1) come from their resistance to the removal of electrons, large positive I values. In short, the values of A for anions would play the same role as the fourth ionization potential of A13+.They would tell us what we already know, that anions will be electron donors, or bases. Our ignorance of A values for anions is therefore not so serious. But we would still like to have some numbers for rating anions, both as to x" and to 7. An equivalent statement is that we would like to know the magnitude of the HOMO-LUMO gap without the complication of the excessive electron-electron repulsion. One way to do this might be from an analysis of vis-UV absorption spectra. But this appears to be hopeless. We can only measure such spectra in condensed phases. But in solution, or in the solid state, we generally observe charge-transfer spectra in which an electron is transferred from the anion to the environment. A more promising possibility is the measurement of optical polarizabilities. There are some problems in that the measured property (the refractive index) must he partitioned into contributions by the individual ions. But this ~ r o h l e mseems to he solvable. since the oolarizahilities of monatomic ions can also be calculated theoretically (22). At present, however, there is little data available on ~olvatomic ions. One approximation that can be made for a number of ions of interest is to assume a proportionality between 7 for an anion and 7 for the corresponding radical. I t may seem strange to use this procedure since it has already been stated that for radicals (I - A) is simply the mean interelectronic repulsion, whereas for ions we want the HOMO-LUMO energy gap. The basis for the approximation is that the size

-

'

No doubly charged anions, not even 02-,are stable in the gas phase. Volume 64

Number 7

July 1987

565

of an atom or molecule largely determines both the mean electron repulsion and the energy gap. The iodide ion is larger than the fluoride ion. This makes the mean interelectronic repulsion smaller and also makes the polarizability large^.^ Also a delocalized anion such as allyl, C3H5-. will have a smaller electron repulsion and a larger polarizability than a similar, but localized, ion such as P~OPY C~d,V . Table 3 gives some results for q for radicals, Y, assumed equal to those of the anions, Y-. The values are generally as expected. The orders are F- > C1- > Br- > I-, and F- > OH> NHz- > CH3-. However, the value for H- is definitely anomalous. The polarizability criterion would make H- very soft, in agreement with its chemical behavior (22). Though differently defined, the values of q in Tahle 3 serve the same purpose as those in Tables 1 or 2. Small values mean good stabilization by both polarization and delocalization. Even a hack-bonding is possible in molecules like AgCN, provided the a bond is synchronized with the a bond, as in

Hyperconjugation is another way in which an anion can accept electrons, without the penalty of a double negative charge. An example is

+Ag-Si-C1

c1-

IC' Tahle 3 also gives results for the x0 values of the anions, assumed to be the ionization potentials of the anions, ,yo =I. Since we already know that anions will he almost pure electron donors, this is the number that characterizes the effective electronegativity for the various ions. In the same way, for the cations of Tahle 1 we may set ,yo = A for ordering purposes. The cations will he almost pure electron acceptors. As expected, the fourth ionization potential of A1 plays no role in its chemistry when this procedure is used.3 I t is helpful to consider briefly the formation of the coordinate covalent bond between two ions, say Na+ and Br-. Nat(g) + Br-(g) = NaBr(g)

(17)

The resulting NaBr is the same as if it had been formed from Na and Br atoms. Not surprisingly, the usually semiempirical MO analysis of the bond in NaBr contains only I and A values for the atoms (9). Solvatlon Eflects So far only isolated (gas phase) systems have been considered. But chemists more often do solution chemistry. What effect does the solvent have on y, and q? This question may he considered to be the same as asking for the influence of solvents on I and A. Taking water as the most important solvent, and letting M be a chemical species, we have M(aq) = Mt(aq) + eC(g)

AG~

(20)

It is interesting to note that classically charged repulsions over a sphere depend on 1/R, where Ris the sphere radius. The polarizabiiity is given by 4aR3/3 for a conducting sphere. We must be careful not to compare two molecules,or ions, using ,yo = lor A for one, and x0 = (I+ A)/2 for the other. 566

Journal of Chemical Education

x0.eV

3.40 1.83 0.74 0.08 3.62 2.30

F

OH NH2

CHn CI

SH PHs Br

1.25 3.36 3.06 0.74

I

H

CHaS

1.9 -0.3

K& CsHs NO*

1.1

3.1

?.eV

7.0 5.7

5.3 4.9

4.7 4.1 4.3 4.2 3.7 6.8 3.1 3.6

4.1 3.9

Free energies of hydration of ions can be found if we know the absolute potential of the hydrogen electrode (20). Fortunalely there is now nearly universal agreement on a value of 4.50 V for the Eo of reaction 21. This enables free energies of hydration of individual ions to he calculated and, therefore, values of I' and A' (24). When M is neutral, I' is lower than I by 2-4 eV. Similarly A' is higher than A by 2-4 eV. For neutral molecules (I' + A1)/2 is nearly unchanged in solution, compared to ( I A)/2. For cations x0 is decreased by about 3 eV, and for anions xo is increased by similar amount. Thus cations are poorer electron acceptors, and anions are poorer electron donors in solution. The ions are stabilized by solvation, as expected.

+

Redox Reactions Values of (P - A912 = n become very small for neutral molecules. This suggests great softness br easy transfer of electrons in both directions. This is true in a sense, since reactions 18 and 19 certainly occur more easily in solution than in the gas. But we must he careful to distinguish between full transfer of an electron and the partial transfer characteristic of Lewis acid-base bonding. The full transfer of an electron. as in reactions 18 and 19. corresponds to oxidation or red&tion. In fact -I' and A; correspond to the absolute one-electron oxidation and reduction potentials of the species M (24). In a few cases they can be measured by the usual electrochemical methods (and the absolute potential of the hydrogen electrode). ort two species, MI and Mz, complete transfer of one electron will occur more or less readily.

(18)

P

If we know I and A in the gas phase for the molecule M, we can calculate P a n d A' from the free energies of hydration of M, M+,and M-. If M is neutral, then solubility data will give us A G (23). ~ M(g) (1atm) = M(aq) (1M)

Table 3. Parameters for Some Radicals, Y, Assumed Equal to Those for Anions, Y-

For most species reaction 22 is too slow and irreversible to give meaningful electrode potentials. Still, such single-electron transfers (SET) are part of the mechanisms for many inorganic and organic reactions (25). They occur in solution, hut not in the gas phase, consistent with a low value of q. But Lewis acid-base reactions are quite different. Since A and B remain bonded together in A-:B+.. onlv dinoles are created, and not separated charges. The solvation energy of a polar molecule is much less than that of an ion, 0.1-0.5 eV instead of 2-4 eV. Therefore, the large changes in I' and A' are not relevant. The xas nhase values of n are much closer to the appropriate valuis. i n principle, sd~vationeffects on polarizability and vis-UV spectra would give approximate corrections to q.

" .

Local Hardness and Soflness

The quantities x and 7 are glohal properties, characteristic of the entire molecule, and not of particular orhitals or atoms. In fact the chemical potential, p = - X, is constant everywhere within the molecule. But it is well known that different parts of a molecule have different reactivities. For example, the thiocyanate ion, NCS-, reacts a t the nitrogen end with hard Lewis acids and a t the sulfur end with soft acids. Using density functional theory, it has been shown that the reactive sites in a molecule are determined by what Parr and Yang (26) call the fukui functions, f. There are three different fukui functions, f ,f+,and f0, depending on whether the molecule is acting as a nucleophile, an electrophile, or as hoth. To a good approximation, it turns out that

Here PLUM^ and p ~ o are ~ the o normalized electron densities of the frontier orhitals. If electron transfer is im~ortant. then chemical reaction occurs a t the site where j has i& largest value. unlike the chemical potential, the hardness is not constant within a molecule, hut is a function of position (27). The consequences are easier to see if a related quantity, C, the local softness is used (28). The global softness, o is set equal to 117).Then C is equal to fa. In the thiocyanate ion, for example, we need to know the mathematical form of the HOMO. Bv sauarine this. we obtain .ounwn .. = ,f-. An ah i ~ i t i o c a l c ~ a t i ofor n NCS- gives the wave function for the HOMO as (29)

where $ is a suitable valence-shell atomic orbital. We see that P H ~ M Ois much larger on sulfur than on nitrogen. Therefore, soft electrophiles will react a t sulfur. From the total electron density, however, nitrogen has a larger negative charge than sulfur, -0.68 e vs. -0.25 e. Therefore, hard electrophiles, whose reactions are controlled by electrostatics, will react a t nitrogen (30). Concluslon

In the foregoing we have tried to show how the new concepts of absolute electronegativity and absolute hardness have been derived. Absolute hardness, which is well defined, is found to he identical with the old concept of chemical hardness, defined qualitatively. The HSAB Principle can he theoretically justified. The new ideas are shown to he compatible with MO the-

ory. Indeed they complement the theory in a novel way, as shown in Figure 2. They seem to have promise for extending the usefulness of the molecular orbital approach. The overall goal is to predict, as far as possible, the reactivity of any chemical species from its individual, independent properties. The properties I and A seem to have special significance, though density functional theory suggests the use of their sum and difference. While we are well supplied with Zvalnes for manv svstems. there is still a ereat shortage of A values. ~articula;lineededarenegativevalues of A. 1 t k hoped that new ex~erimental methods will make these availAcknowledgment

I wish to thank R. G. Parr for rekindling my interest in hard and soft acids and bases. I also wish to thank M. Berkowitz and W. Yang for stimulating discussions. Somewhat belatedly, I would also like to acknowledge the support and encouragement of C . K. Jorgensen, R. F. Hudson, G. Klopman, and S. Ahrland during the early days of HSAB. Finally, I thank J. 0 Edwards for his initial stimulating ideas. Literature Clted I. Peara0n.R. G. J.Am. Chem. So?.1983,83,3583.

2. Pearson, R. G. Hard and Soft Aeida ond Barn; Dowden, Hutchinson and Raar: Stroudrbulg, PA, 1973. 3. Parr,R.G.:Donnell~,R.A.;Lew,M.;Palke, W.E. J.Chem.Phys.l978,68,3801:Parr, R.G..Bartolotfi, J. J.Am. Chem Sor. 1982, I M , 3801. 4. Mulliksn, R. S.J Chem. Phys. 1934.2.782. 5. Pau1ing.L. TheNolure 0 1 t h ~ChemicoiBond:CornellUniverjity:Ithaca, NY, 19M):p 88.

....,

13. Psrr,R.G.;Yang, W.J.Am. Chem.Soe,1984,106,4049. 14. Pesrson, R. G. Inorg. Cham. 1984.23.4675, 15. Gullanova, E. N. Uspekki Khimii 1368.37, 1981. 16. K1opman.G. J. Am. Charn.Soc. 1964,86,1463. 17. Jorgenaen, C. K. Struct. Bonding (Berlin) 1967.3,106. 18. Robin. M. B. Higher Excited States of Poiyotomic Moierulea:Academic: New York, 147d.V"l ., . 1., " " A 6 19. Pearson, R. G. Symmetry Rules for Chemical Rsoclio~: Wilsy-Interscience: New Ynrk 19%~,Chanler ~~~~,~~ .-... ..I 20. Dswsr, M. J. S. J. Am. Chom. Sac. 1952,74, 3341. 3357. 21. Fukui, K.;Fujimato, H. Buil Chem. Soc. Jopon 1968.41.1989: 1969,42,3399. 22. Jorgensen. C. K. SLrurl.Bonding (Bwiinl 1966.1.234, 23. Hine,J.: Mookerjl. P. K. J. Org. Chem 1975.40.292. 24. Pesnon. R. G. J.Am.Chem.Soc.,1986, I06.61W. 25. Ebor8on.L. Ado. Phys. Org. Chem. 1982, 18.79: Kaim, W. Acc. Cham. Rex. 1985.18, 1W. 26. pa;, R. G.;Yang, W. J.Am. Chem. Soe 1984,106,4049. 27. Berkouitr,M.;Ghash,S.K.;Parr,R. G.J. Am. Chsm.Soc. 1985,107,6811. 28. Yang, W.: Psrr,R.G.Proe.Not.Aeud.Sci. 1985.82.6273, 29. Joreensen. K. A,: Lawesson,S. J.Am. Chem Soc. 1984,10&46S7.

-

30.

For a full discmion of charge and orbital controlled reactions

see Klopman, G.

Chsmieoi R~orliuityend Raacfion Polhs; Wiley: NewYork, 197?;Chapter 4.

Miriam Reiner Receives Iota Sigma Pi Professional Excellence Award Miriam Reiner will receive the Professional Excellence Award sponsored by Iota Sigma Pi, a professional society for women chemists, at their national convention this month in Minneapolis. Miriam Reiner was horn in Baltimore and received both a BS and MS from Columbia University and a PhD from Georgetown University. She is the author of the Monuol of Clinical Chemistry, which, published in 1941, became the practical working handbook for ~rofessionalclinical chemists evervwhere.She was the first editor of Standard Methods in Clcntrnl Chemi.,tq and is renou,ned fur her early work m elecrrophorenir. Heiwr a h served for 20 year4 as rhr Chief of Chrmistry Diwsirm c.f D.C. General Hospital in \Va.;hingon. DC nnd has brrn extremely artwe in horh rhr American retired and l i b ing in Washington. DC. hwrialion of Clinical Chemirrs nnd Iota Sigma Pi. She is c~~rrentl? ~

Volume 64

Number 7

~

July 1987

567