A Quasi-Thermodynamic Theory of Nucleophilic Reactivity - American

13

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on December 18, 2015 | http://pubs.acs.org Publication Date: July 1, 1987 | doi: 10.1021/ba-1987-0215.ch013

A Quasi-Thermodynamic Theory of Nucleophilic Reactivity R. F. Hudson Chemical Laboratory, University of Kent, Canterbury, Kent, England

Nucleophilic reactivity is related by a semiempirical equation to solvation energy and electron affinity of the nucleophile and the dissociation energy of the bond formed. A general equation, which shows that nucleophilicity is a function of bond formation in the transition state, reduces to the Swain and Brønsted equations under limiting conditions. The abnormally high reactivity of so-called αnucleophiles is examined. Accordingly, the α effect is shown to be proportional to the extent of bond formation as given by the Brønsted coefficient β. A maximum α effect when β = 1, that is, when bond formation is complete, is supported by experimental data and by thermochemical calculations involving "normal" nucleophiles and αnucleophiles. Calculations at the G-4.31 and G*-6.311 levels shed further light on the origin of the α effect.

T H E C O N C E P T O F N U C L E O P H I L I C R E A C T I V I T Y is central to organic chem istry in that most reactions involve electron transfer in the transition state to some extent. The classical theory of Ingold et al. (J) invoked the idea by assuming that H O " (very basic) was more nucleophilic than H 0 (weakly basic), without giving any clear-cut definition of nucleophilic reactivity. Indeed, it was known at the time, largely through the work of Conant and co workers (2, 3), that some ions, for example, I and B r were very nu cleophilic but very weak bases. However, the idea persisted for some time, largely through the influence of the Br0nsted theory (4) that nucleophilic reactivity (and also leaving-group ability) depended on proton basicity. A breakthrough came when Swain and Scott (5) proposed a two-param eter equation that calibrated the reactivity of nucleophiles by reference to their rate of reaction toward methyl iodide, taken to be a "standard" elec trophile. This equation was based, in effect, on the well-known order of reactivity in S 2 reactions I" > B r " , C l > F " and on the work of Foss (6), 2

-

-

-

N

0065-2393/87/0215-0195$06.00/0 © 1987 American Chemical Society

In Nucleophilicity; Harris, J., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1987.


196

NUCLEOPHILICITY

which showed that reactivity toward divalent sulfur correlated closely with the redox potential of that nucleophile. Although the Swain equation made a very important contribution, it led to some confusion because it was originally applied to all types of reactions including alkylation, acylation, and sulfonylation. The nucleophilic order is highly dependent on the nature of the substrate, and the equation was modified in the Swain-Edwards four-parameter equation (7). The main drawback of these linear free-energy relationships is that they do not relate to reaction mechanisms. Curiously enough, like the original Br0nsted equation, the main objective appeared to be the correlation of rate data rather than the interpretation of reaction mechanisms. This deficiency was partly remedied in the concept (8) of hard-soft acid-base (HSAB), which was in effect a qualitative extension of the Swain-Edwards equation but was more powerful in the sense that different types of reaction were related to the hard-soft classification, and the concept therefore has a wide application in organic synthesis and inorganic equilibria. Our work evolved from early investigations into the mechanism of hydrolysis of acyl chlorides (9-11) and the reactivity of nucleophiles toward organophosphorus compounds (12). I was intrigued at that time by the fact that some nucleophiles rapidly dealkylated phosphate esters and hence were important in deprotection in nucleotide chemistry, and other nucleophiles were rapidly phosphorylated, and this finding is important in the search for antidotes for the nerve gases and also in predicting the reactivity of organophosphorus insecticides. The orders of nucleophilic reactivity for alkylation and acylation were found to be quite different (13, 14) and in subsequent work (15) this finding was related to the extent of bond formation in the transition state as given empirically by the Br0nsted coefficient, β. Previously, this difference was used to predict the position of bond fission in the alkaline hydrolysis of phosphinate, phosphonate, and phosphate esters (12). Jencks and Carriuolo (16) came to similar conclusions around the same time in outstanding work on the acylation of p-nitrophenyl acetate. So that a simple interpretation of nucleophilic reactivity could be de rived, (17), the approach developed by Polanyi and Evans (18) in their famous work on transition-state theory was used. The reactivity of a series of nucleophiles toward a given electrophile was represented by using recogniz able energy terms and proceeding as follows. First, the equilibrium for the addition of a nucleophile, N " , to an electrophile, E , is +

+

Ν" + E ; p = ± N - E The free-energy change, AG° is estimated in terms of experimental quan tities by adopting the following thermodynamic cycle.


13.

HUDSON

A Quasi-Thermodynamic Theory of Nucleophilic Reactivity 197 AG°

N-(g)

•


AG°

N°(g) + e-

4

The following terms are involved: AG° is the free energy of solution N " ( — A G ) , AG° is the free energy of solution E ( — A G ) , AG° is the electron affinity of E°, AG° is the electron affinity of N° (E ), and AG° is the bond dissociation energy (D _ ) and the associated entropy difference (S _ - S o-S o). Electron affinity is an enthalpy term, but the entropy differences S _ — S and S — S are negligible. The required free energy change, AG°, is then given by AG° = A G + AG ' + AG _ o + E - rfS o + S _ - S _) - D _ - T [ S _ l

S

+

N

S

2

E

4

N

N

N

3

N

5

E

N

E

E

e

E +

S

N

E +

E + + e

E

N

N

e

N

N

E

N

E(solv)

S

~ S ( ] = AG + E - D _ - 7TS _E(solv) ~~ ^N-(g)]' Because A G values for a series of nucleophiles, N , and a given electrophile (E) are being compared, terms involving Ε only are constant. Thus, E

g)

N

N

N

E

N

0

-

AG° = A G * + £ N

N

- D _ - T[S _ N

E

N

In the derivation of all L F E R s changes in δ _ be small as Ν " is varied and hence Ν

AG° - A G

S N

+ E

N

E(solv)

Ε($ο1ν)

- S _] + constant N

- S _ N

(g)

can be assumed to

- D _ + constant N

E

So that this approach can be adapted to the rate of analogous process, that is, the reaction between N " and E - X , the bond is assumed to extend to the critical distance characteristic of the transition state. The nucleophile then interacts with the electrophilic center with transfer of charge Ze. This reaction leads to partial bond formation and partial desolvation involving free energy changes yD _ and — a A G , respectively. The free energy of activation, A G * , is then given by s

N

E

AG* - aAG

N

s N

+ β Ε — yD _ Ν

N

E

+ constant

where β £ is the energy change produced by the "partial" electron transfer Ze. So that this equation can be applied to experimental data, relative magnitudes of α, β, and 7 have to be found. As a first attempt to interrelate these coefficients, an electrostatic model was adopted for the desolvation and electron-transfer terms. Ν


198

NUCLEOPHILICITY

The free energy of transfer of an ion from gas phase to solution, that is, the free energy of solvation, is given by the Born equation (19, 20):


N

(2Dr)

The equation can be applied with reasonable accuracy to changes in charge, Z, which are of concern in the present application, and to changes in ionic radius, r. The equation is difficult to apply when different solvents are employed because the value of the dielectric constant in the neighborhood of an ion is difficult to calculate. The change in electrostatic energy on removal of charge Ze from N ~ can be evaluated by using the energy required to remove this charge from a sphere (21), that is β/

= Z*E

Ν

N

Bond dissociation energies are given quite accurately by the Morse function (22, 23), but in view of its complexity it is assumed that

With η = 2, equation 1 can be derived: 2

2

A G * - (2Z - Z ) A G * - Z ( D _ - E ) + constant N

N

E

(1)

N

This equation has been examined for several values of Z, but the equation does not appear to represent the experimental S 2 reactivities particularly well (Table I). In an alternative treatment (17), again desolvation is assumed to precede bond formation, and electron transfer and desolvation are assumed to be N

Table I. Calculated Values of ΔΕ* from Equations 1 and 2 and the Free Energy of Reaction, AG° , Compared to Swains JV Parameter C

F Cl Br I OH SH

112.0 84.6 67.0 57.2 92.6 72.0

IN

AG/

83.5 88.2 81.6 74.6 35.0 46.0

96 64 58 46 105 -73

AG°C

67.5 67.6 68.6 63.4 47.4 47.0

a

L

r

η

calcd

(2.00) 3.35 3.95 5.00 4.50 5.60

(2.0) 3.6 3.8 5.0 3.9 5.5

_ 1

2.00 3.05 3.85 5.00 4.25 5.10

N O T E : Energies are given as kcal m . - A G * = 0.07 [ ( A G + £ ) - 0.33D _ ] from equation 2 with α = 0.07 and 7 = 0.023. - A G * = 0.17 [ A G - 0.7 ( D _ - E ) J ; cf equation 1.

a

S

N

b

N

N

C

s

n

N

C

N


13.

HUDSON

A Quasi-Thermodynamic Theory of Nucleophilic Reactivity 199

represented by a single parameter, that is, α - β. The equation then reduces to A G * - a ( A G * + E ) - yD _ N

N

N

(2)

+ constant

E

where 1 > α > 7. This equation involves the ionization potential of the solvated nucleophile, A G + E , and partial bond formation as opposing energy terms. Several interesting limiting conditions occur for this equation. The first limiting condition occurs when the bond formation is small (7 —• 0) and S


N

N

AG* - a(AG

+

+ £ ) + constant

N

(3)

N

That is, the reactivity is related to the redox potential of N " , and equation 3 reduces to the Swain equation (5): log (k/k°) = sn A second limiting condition occurs when the bond formation is large (7 — • 1) and

A G * - A G * + E - - D _ + constant N

N

N

(4)

E

That is, the reactivity is given by the affinity of the nucleophile toward the reaction center under consideration. A third limiting condition occurs when similar nucleophiles are in volved; for example, for a series of ions of the general structure A O , the bond energy term, D _ , may be treated as a constant (cf equation 3). Similarly, for a combination with a proton -

N

E

AG

H

= (AG * + E ) + constant N

N

(5)

Combination of equations 3 and 5 gives AG* = a A G

H

+ constant

(6)

That is, the extended B r 0 n s t e d relation (24) l o

g

k

K

= $nucV a

+ constant

Numerical reactivity constants can be derived from equation 2 by inserting empirical values of α and 7 with the restriction that α > 7 because 7/0: is a measure of the extent of bond formation in the transition state. (7/a = 1 for complete bond formation.)


200

NUCLEOPHILICITY

With values of α = 0.07 and y = 0.023, the calculated reactivity at a saturated carbon atom is compared with Swains η values in Table I . When the calculated values are scaled to 2.0 for F " , a set of constants AG in reasonable agreement with the experimental values (n) is obtained. The quantitative use of this equation is, however, limited, but this usage does lead to qualitative conclusions of importance that are complementary to the well-known theory (8) of Η SAB. Thus, according to our general treatment, the relative reactivity of two nucleophiles is given by the relative magnitude of ( A G + £ ) and D _ . However, the relative reactivity is also given by the relative magnitude of α and 7; that is, the relative reactivity is a function of the extent of bond formation (and hence of the Br0nsted β ) . This result is shown diagrammatically in Figure 1. Accordingly, the relative reactivity of two nucleophiles, for example, I " (soft) and O H ~ (hard), increases as the selectivity increases. As the influence of the third term becomes significant with the increase in bond formation, a reversal occurs from the "soft" order ^ _ / ^ _ > 1 to the "hard" order K O H ^ R O - > 1 ( β 0.15). This effect is much more pronounced in reactions of hydrogen, for example, in the base-catalyzed elimination of B u C l , fc _ fc _ > 1 ( β 0.15), whereas in general, k Jk _ 1 f° β-eliminations. c a l c d

S


N

N

N

ηυε

Η

ηιιε

t

>

m

r m

o

s

RS

R0

t

RS

Figure 1. Change in selectivity with degree of bond formation in the transition state (β).


η υ ε

E

13.

HUDSON


At a more theoretical level, nucleophilic reactivity can be treated by the polyelectron perturbation method (25), which in its simplest form gives the perturbation energy in terms of a first-order (Coulombic) term and a secondorder term involving orbital energies c^ and a (Figure 2). Subsequently, this equation was adapted by Hudson and Filippini (27) and independently by Klopman et al. (28) to the problem of enhanced nucleophilic reactivity. This problem is particularly thorny, and it will now be discussed in some detail.


k

ak

(σ·)

ak

(H )

+

Figure 2. Perturbation treatment of the a effect. (Reproduced with permission from reference 48. Copyright 1973 Verlag Chemie). According to my treatment, the α effect is attributed to electron-pair repulsions that cause orbital splitting (Figure 2), with a consequent increase in perturbation (i.e., stabilization) due to a decrease in the ctj — o^ term. However, why this effect does not also affect the corresponding pK values to which the α effect is related is not clear. In fact, adjacent lone pairs produce large decreases in the rate of proton removal from pyridine and other nitrogen heterocycles (29, 30). Considering the reverse process, this effect should lead to an increase in pK . This explanation of the α effect has been criticized extensively in recent years (31-33). a

a


202

NUCLEOPHILICITY

According to my treatment, the magnitude of the α effect increases with the extent of bond formation in the transition state as represented by the Br0nsted, β , parameter. This finding is in accord with experimental obser vations, and Aubort and Hudson (34) showed some time ago (Table II) that the α effect for p-nitrophenyl acetate ( β - 0.8) is much greater than that for an alkyl bromide ( β Û.3). Dixon and Bruice (35) showed a similar effect for the reaction of hydrazines with a wide range of electrophiles. η υ ο

η υ ε


ηικ?

Table II. Comparison of the α Effect for Benzyl Bromide and p-Nitrobenzyl Bromide with the α Effect for p-Nitrophenyl Acetate (PNPA) ΔΔ /og k PNPA RBr

Ratio

Nucleophile, R

Reference

CH3COCHNO-

24

0.60

2.00

3.3

RCONO(CH )0-

24

1.10

2.10

2.1

25

1.70

3.50

1.9

3

H0 2

The logical extension of this relationship is that the α effect is a max imum when β = 1.0, that is, when bond formation is complete. This relationship means that the α effect should be observed in equilibria as well as in kinetics. This proposal was suggested by Hine and Weimar (36), who made thermochemical calculations of the affinities of some anions including H 0 and H O toward carbon and hydrogen for which an α effect of the order of 10 for the equilibrium was found. Moreover, Jencks and co-workers (37, 38) measured the equilibrium constant for the acylation of N-methylhydroxamic acids and obtained an experimental value of approximately 10 for the equilibrium α effect. This value is considerably less than the experimental value obtained from the rates of acylation. The apparent anomaly may be due to the two-stage process that is usually assumed for acylation: -

2

-

6

2

κ, AO" + RCOX^

o^ R-Ç-OA X

^ R-CO-OA + X "

The kinetics refer to the formation and subsequent decomposition of a (charged) tetrahedral intermediate, whereas the affinities are given by the overall equilibrium constants Kj and K . I suggest (vide infra) that the affinity of a nucleophile is highly dependent on the Coulombic interaction energy, and this dependence could lead to a larger α effect for the rate of acylation than for the equilibrium. In recent work (39) on isothiocyanates, oximes were found to add readily to acyl isothiocyanates to give intermediates, for example 2


13.


HUDSON

Nz:N-OH + C H C(0)N=C=S==


6

where k » addition:

X

V

= N-0-C(S)NHC(0)C H

5

6

1, whereas phenols of comparable pK show no tendency toward a

^ ^ " "

O

H

+

C

6

H

5

C

( ° )

N

=

C

=

S

4

OC(S)NHC(0)C H 6

5

where it « 1. To explain this remarkable difference in the behavior of oximes and phenols, a hypothetical series of processes was assumed and then the first law of thermodynamics was applied. Thus, for the addition of an oxime to the isothiocyanate, the following processes can be postulated: R C= N-OH 2

N

R C=N-0" + H

v

PhCONCS + H + v — * Ph-CONH-C Ph-CONH-C

+

+

2

+

=S

=S + R C = N - 0 ^ = ^ = ^ P h C O - N H - C S - O N = C R 2

2

Although the purpose of this postulate is to explain the reaction affinity, the postulate is a reasonable reaction mechanism. In the presence of triethylamine, both oximes and phenols are benzoylated by reaction at the carbonyl group:

X

V

x

^ ^ ~ Ο" + C H C ( 0 ) N = C = S— 6

5

(^^)-OC(0)C H 6

5

+ NCS"

This example shows the regiospecificity of nucleophilic attack. The observed equilibrium constant, K, is given by Κ

=

K H K J ^

For two nucleophiles with similar p K values, for example, an oxime and phenol, K is constant, K is common, and hence Κ is determined by K . In other words, the affinity of the oxime toward a carbonium center is greater than the affinity of a "normal" nucleophile of comparable pK . To generalize, an α effect will be observed in an equilibrium when the relative proton affinity, A G ° , is greater than the relative affinity toward the a

H

Y

2

fl

H


5

204

NUCLEOPHILICITY

electrophile, A G . This statement is supported by the thermochemical calculations and ab initio calculations at the G-4.31 level (Table III). From the estimated values of the affinities toward carbon and hydrogen from ther mochemical data, A G ° - A G ° for C H 0 ~ and C H 0 ~ , two normal nu cleophiles of very different basicity. However, A G ° - A G ° = 4.8 kcal/mol when C H 0 ~ and H 0 ~ are compared; this result corresponds to an α effect of 10 at 298 °C. This value may be compared with the experimental value of the α effect of 10 for the α effect in the reaction of p-nitrophenyl acetate with H 0 " . The value of β is found to be 0.65 from the log k-pK slope at pK -12, that is, for H 0 . Thus, for complete bond formation, a value of 10 would be found for the α effect, if this effect is assumed to be proportional to E

H

C

3

2

H

3

C

2

35

24


2

a

3 7

fl

2

2

β.

Table III. Highest Occupied Molecular O r b i t a l ( H O M O ) Energies, Mulliken Charges, q , and Calculated and E x p e r i m e n t a l Proton and M e t h y l Cation Affinities of Some Oxyanions 0

Proton Affinity AGj/

ΣΗΟΜΟ

Methyl Cation Affinity A G °

Electronic Charge on Oxygen q

C

0

Oxyanion

G-4.31

G*-6.311

G-4.31

Exptl

G-4.31

Exptl

G-4.31

G*-6.311

HOCH 0H0 FOHC0 "

-0.0340

-0.0483 -0.0773 -0.0942 -0.1514

426.0 409.8 387.4 360.5 360.0

390.8 379.2 379.4

292.8 279.1 259.6 235.4 229.8

276.3 267.6 272.6

-1.144 -0.949 -0.607 -0.471 -0.788

-1.193 -0.859 -0.614 -0.457

3

2

2

-0.0635 -0.0868 -0.1371 -0.1510

345.2

233.1

N O T E : H O M O energies are in hartrees. Mulliken charges are in units of electrons on the nucleophilic atom. At 0 K , the calculated affinities were uncorrected for zero-point vibration. T h e experimental affinities were at Δ / / for the process N " + A — • N X (A = Η and C). The affinities were in units of kilocalories per mol. +

2 θ 8

When the origin of the enhanced affinity of the a-nucleophile toward the electrophilic center or, alternatively, the enhanced affinity of the normal nucleophile toward the proton is studied, the equilibria can be treated by a classical thermodynamic argument as follows (40). Consider the equilibria Nf

+

K

+ E

N - + E

+

2

^

l

\ N

2

r

+

E

Nj" + H ^

S N -E 2

N -+ H * ^ 2

K l

2

"

sN ^ H

"

NNL-H

Each process is imagined to involve (1) desolvation, (2) electron transfer, and (3) bond formation. Thus, according to AG° = -RT

In Κ = Δ Η

Ν

+ E

N

- D

N E

+ ΣΕ

+

+ ΓΣΔ5

(9) +

where Δ / / , E , and D _ have already been defined (see equation 1); ΣΕ represents energy terms for Ε that are constant when two nucleophiles are Ν

N

N

E


13.

HUDSON


compared, and ΣΔΞ is the net entropy change in the reaction, which can be neglected in the following treatment. When this equation is applied to previously mentioned equilibria RT In ψ

- R r i n ^ L = (D _ H

=

- D _ ) - (D .

Ni

H

(AD _ H

N

-

Na

E

-

D _ ) E

Na

AD _ ) E

N

where N represents a normal nucleophile and N an a-nucleophile. Thus, an α effect will be observed in an equilibrium when the difference in bond dissociation energies of a normal and an α-nucleophile joined to a proton is greater than the corresponding difference when the two nu cleophiles are joined to the electrophilic center under consideration. In a previous note presenting a perturbation treatment, the α effect was attributed to a combination of electron-pair repulsion and Coulombic inter action with the proton and the electrophilic center. This explanation can be examined further by reference to the molecular orbital data in Table III. A decrease in Σ Η Ο Μ Ο (i.e., an increase in ionization potential) of a normal nucleophile is accompanied by a decrease in q , the charge on the nu cleophilic atom. However, substitution at the nucleophilic atom to form an anucleophile, for example, H 0 ~ , produces a large decrease in q for a smaller decrease in Σ Η Ο Μ Ο . For example, Σ Η Ο Μ Ο for H C 0 ~ is considerably less than Σ Η Ο Μ Ο for H 0 " , but the negative charge is greater for the H C 0 " ion. This relationship is shown diagrammatically in Figure 3, where the energy of the H O M O is plotted against the charge density, q , on the nucleophilic oxygen atom. If an extrapolation is made through the points for H C 0 ~ and C H 0 ~ , that is, the two normal nucleophiles, the H O M O energy is approximately 5.0 eV greater than that predicted for H 0 ~ and approximately 5.7 eV greater than that predicted for F O " . This finding means that the electron affinity of H 0 is much less than expected on the basis of the nuclear charge. These calculations suggest that the increased value of A D relative to AD may be explained in terms of bond polarities. The abnormally large decrease in negative charge, q , for H 0 " reduces the Coulombic contribu tions to the energies of the H - O and C - O bonds. In view of the fact that H - O bonds are more polar than C - O bonds, a consequence partly of the reduced internuclear distance, this reduction in Coulombic energy is greater for interactions with the proton. Therefore, O H ~ (or C H 0 ~ ) has an abnormally high affinity for the proton, and as a consequence, H 0 ~ , and other α-nucleophiles, has a greater relative affinity for carbon (and for other electrophilic centers). This finding appears to form the basis of the apparently high reactivity of a-nucleophiles, which is intrinsic to the reagent and should be observed in gas-phase equilibria (see Table III) as well as in solution kinetics. l


N i

2

0

2

0

2

2

2

Q

2

3

2

2

H N

C N

0

2

3

2


206

NUCLEOPHILICITY


£-3lG

Level

12

4

.6

.8

1.0

1.2

Figure 3. Relationship between the calculated HOMO energy and total charge on the terminal oxygen atom, q , of several oxygen nucleophiles. 0

Recent work (32, 43) has cast doubt on this conclusion. De Puy et al. have shown, by product analysis of reaction of H 0 ~ with esters in the gas phase, the absence of a kinetic α effect. These reactions are generally collision-controlled, and hence rate differ ences are due to probability factors. Under these conditions, reaction selec tivity due to activation energy differences disappears, although as discussed previously the α effect will manifest itself in differences in the corresponding equilibria. As a consequence, the α effect should be solvent independent or nearly so. However, recent work (44, 45) has shown appreciable increases in the α effect of oximes as the concentration of dimethyl sulfoxide increases. How ever, this increased α effect reaches a maximum at approximately 50 mol %, and the values in water and ( C H ) S O appear to be very similar. In other words, on this limited evidence, the α effect is the same in pure solvents but may change appreciably in solvent mixtures. Liquid mixtures are notoriously complex, and hence we suggest that the increased α effects are due to changes in liquid structure, which are analogous to phase changes on a micro scale (cf micelles). In conclusion, the α effect is attributed to the cooperative effect of two terms: (a) orbital splitting, which determines the H O M O and the ionization potential of the nucleophile and (b) a Coulombic term, which produces bond polarity. The influence of these terms on the α effect has been analyzed 2

3

2


13.

HUDSON


recently by Laloi-Diard and Minot (46) by perturbation theory, which is an extension of our earlier treatment (26). The balance between these two terms, which is different for the combination of a nucleophile with a reaction center (electrophile) and a proton, produces the α effect. A striking example of this theory is the large α effect (ca. 10 ) of pyridine N-oxides in contrast to the "normal" behavior of trimethylamine N-oxide and phenoxide (47). According to my explanation, Ρ - Ρ repulsion in the phe noxide and the inductive (Coulombic) effect in the aliphatic amine oxide alone do not produce an α effect. However, the combined action of the inductive effect and Ρ - Ρ repulsion in the aromatic N-oxide produces the observed α effect. 3


π

π

π

π

Acknowledgmen ts I thank S. Wolfe for his help and encouragement in the course of this work, which was developed during a stay at Queens University, Kingston, D . J. Mitchell for permission to use his computational data, and D . N . Hague and D . P. Hansell for helpful discussions. Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.

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27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46.

NUCLEOPHILICITY

Hudson, R. F.; Filippini, F. Chem. Comm. 1972, 522. Klopman, G.; Tsuda, K.; Louis, J. B.; Davis, R. E. Tetrahedron 1970, 26, 4549. Zoltewicz, J. Α.; Grahe, G.; Smith, C. L. J. Am. Chem. Soc. 1969, 91, 5501. Kauffmann, T.; Wirthwein, R. Angew. Chem. Intl. Ed. 1971, 10, 20. Liebman, J. F.; Pollack, R. M . J. Org. Chem. 1973, 38, 3444. De Puy, C. H . ; Della, E. W.; Filley, J.; Grabowski, J. J.; Bierbaum, V. M . J. Am. Chem. Soc. 1983, 105, 2482. Wolfe, S.; Mitchell, D. J.; Schlegel, H . B. J. Am. Chem. Soc. 1981, 103, 7694. Aubort, J. D.; Hudson, R. F. Chem. Comm. 1970, 937. Dixon, J. E . ; Bruice, T. C. J. Am. Chem. Soc. 1972, 94, 2052. Hine, J.; Weimar, R. D. J. Am. Chem. Soc. 1965, 87, 3387. Gerstein, J.; Jencks, W. P. J. Am. Chem. Soc. 1964, 86, 4655. Sander, E. G.; Jencks, W. P. J. Am. Chem. Soc. 1968, 90, 6154. Hudson, R. F.; Hansell, D. P. Chem. Comm. 1985, 1405. Hudson, R. F.; Hansell, D. P.; Wolfe, S.; Mitchell, D. J.; Chem. Comm. 1985, 1406. Wolfe, S.; Mitchell, D . J.; Schlegel, H . B . ; Minot, C.; Eisenstein, O. Tetrahedron Lett. 1982, 23, 615. Laloi-Diard, M . ; Verchere, J.-F.; Gosselin, P.; and Terrier, F. Tetrahedron Lett. 1984, 1267. Buncel, E . ; Um Ik-Hwan J. Chem. Soc. Chem. Commun. 1986, 595. Laloi-Diard, M . ; Minot, C. Nouveau J. de Chimie 1985, 9, 569. Jencks, W. P.; Carrinolo, J. J. Am. Chem. Soc. 1960, 82, 1778. Hudson, R. F. Angew. Chem. 1973, 85, 63.

RECEIVED

for review October

2 1 , 1985.

ACCEPTED

August

1, 1 9 8 6 .


A Quasi-Thermodynamic Theory of Nucleophilic Reactivity - American

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