Nucleophilicity and Distance - American Chemical Society

14 Nucleophilicity and Distance Fredric M. Menger

Downloaded by UNIV OF SYDNEY on May 5, 2015 | http://pubs.acs.org Publication Date: July 1, 1987 | doi: 10.1021/ba-1987-0215.ch014

Department of Chemistry, Emory University, Atlanta, GA 30322

This paper focuses on the relationship between reactivity of a nucleophile with an electrophile and the distance separating the two species. The relationship, examined by means of rigid molecular frameworks bearing two functionalities at well-defined distances and angles, is shown to be extremely sensitive. Theoretical considerations also support the contention that distance is a key parameter in nucleophilic reactivity. Reactions in solution occur with enzyme-like rates when critical distances are achieved.

O P E N A T E X T B O O K O N O R G A N I C C H E M I S T R Y , introductory or otherwise. You will find information on how nucleophilicity depends on basicity, polarizability, solvent, temperature, substituents, structure of electrophile, and so on. But you will not find much information on how nucleophilicity depends on geometric disposition. Too little is known about the subject. This lack of knowledge constitutes a serious gap in our understanding of chemical dy namics because, as will be shown, distance is critically important to nu cleophilic reactivity. Distance information is required to fully characterize reaction pathways and to interpret structural data on enzymes. How, after all, can a particular arrangement of catalytic groups surrounding a substrate at an active site be evaluated without first understanding the connection between reactivity and alignment? Our interest in nucleophilicity derives in large measure from the amaz ing velocities at which enzymatic nucleophiles attack bound substrates. Chymotrypsin, for example, has a serine hydroxyl that performs a nu cleophilic attack on an amide carbonyl about 10 times faster than the laboratory rate at equivalent p H and temperature (i). A general-base cata lysis by an imidazole ring accounts of 10-10 of this factor; at least 10 remains as a mystery. Why is the chymotrypsin hydroxyl such a powerful nucleophile? Few chemists would answer this question by invoking a mecha nism unique to biology. No reason exists to suspect that enzymes operate by anything other than the principles familiar to every organic chemist. Yet the 8

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0065-2393/87/0215-0209$06.00/0 © 1987 American Chemical Society

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

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interplay of effects that ultimately gives rise to enzymatic catalysis remains a matter of conjecture. Enzyme-like nucleophilicities can be secured in the laboratory via (a) intramolecular systems and (b) judicious choice of solvent. (As will be argued later, these effects are not unrelated.) Two specific examples serve to illus trate the point.

I

+

I

In the first reaction, intramolecular attack by the hydroxyl on the carboxyl carbonyl proceeds 5 Χ 10 times faster than the corresponding intermolecular process (2). In the second reaction, the rate increases 10 -fold upon switching the solvent from methanol to dimethylformamide (3). Ob viously, the huge rate increases in these organic systems do not necessarily prove that similar effects are at work in enzymes. But to be suspicious is quite natural, and many people, too numerous to mention, have pointed out the possible relationship between enzyme catalysis and intramolecularity or solvation effects. The possibility that enzymatic reactivity is indeed related to intra molecularity leads next to an important question: Why are intramolecular reactions often very fast? Unfortunately, no good answer exists to this ques tion. The difficulty is brought forth with a vengence in Kirbys scholarly compilation of effective molarity (EM) values (4) (where E M = fc /fc er)' E M values, which vary from very small (10 M), depend on ring size, substituents, solvent, and reaction type. No known theory can explain—let alone predict—these wild fluctuations. A person is reminded of the first law of sociology: "Some do, some don't". Kirbys compilation probably represents the largest and most variant body of unex plained data in physical organic chemistry. Two recent articles from our laboratories delve into the question of intramolecularity (5, 6). The main postulate of reference 6 is that the rate of reaction between functionalities A and Β is proportional to the time that A and Β reside within a critical distance. Thus, fast intramolecular (or en8

7

intra

int

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Nucleophilicity and Distance

zymatic) reactions are thought to occur when a carbon framework (or a protein structure) enforces residency at critical distances upon two reactive groups. Reference 6 contains (a) evidence supporting the postulate, (b) magnitudes of critical distances, and (c) examples of intramolecular reactions attaining enzyme-like rates when critical distances are imposed. In the remainder of this chapter, important points that, for one reason or the other, could not be fully covered previously are discussed (in ques tion-answer format).


Is It Reasonable to Postulate a Critical Distance? A critical distance is both a reasonable and a time-honored concept. Con sider the cases below in which critical distances have been invoked. (a) The classical theory of Smoluchowski (7) assumes that a reaction between two hard-sphere molecules occurs only when the separation dis tance r reaches R, the "distance of closest approach" (equation 1). Note the presence in equation 1 of the "δ function", which equals either zero or unity: 6(r - R) = 0 if (r - R) > 0; b(r - R) = 1 if (r - R) = 0. k(r) =

(D

(b) Intermolecular triplet-triplet energy transfer is described by the Perrin equation (equation 2) (8). In this model, a donor is quenched if an acceptor at concentration C lies within a critical radius R . A typical do nor-acceptor pair has an R of 13 Â; this value indicates that quenching abruptly ceases when the separation distance exceeds 13 Â. A

c

c

_ /3000 1η ( / A ) Y

3 ( 2 )

(c) In a statistical treatment of intramolecularity, Sisido (9) assumed that a reaction takes place only when the separation between functional groups at the ends of a chain becomes shorter than a distance r . Good fits between experimental and calculated cyclization constants were obtained with an r = 2.3-2.7 À. (d) Electron transfer in any given system occurs, undoubtedly, over a range of encounter distances R. Because each separation distance has its own transfer probability, the rate constant must be obtained by integrating over the equilibrium distribution of distances [equation 3, where R is the separa tion distance of the redox centers and g(Rg) is the pair distribution function]. 0

0

tj

k

{j

= cf^R/g

(RjkJRJ

dR

(j

(3)

Usually, however, the situation can be simplified by assuming an "effective" encounter distance; the observed rate then becomes a function of the rate at this particular separation distance and the work necessary to bring the


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NUCLEOPHILICITY

reactants together (10). Although no rigorous meaning can be given to the effective encounter distance, this distance is often considered to be the "contact" separation of the reactants. The terms "critical distance", "bonding distance", "encounter dis tance", "contact distance", and "van der Waals distance" can be used inter changeably. They all refer to the distance at which a nucleophile and elec trophile initiate bond formation. The longer two species remain at this distance, the faster the rate. 9


How "Critical' Is the Critical Distance? Four cases were just described that treat rate versus distance as if it were a step function. Surely this result is not accepted literally. But because phys ical-chemical data can often be fit to equations that incorporate a step function, the dependence of rate on distance must be very sharp if not exactly a step function. The situation is not unlike that of the "critical micelle concentration" or cmc. A surfactant in water forms large aggregates (micelles) when its concentration reaches the cmc. Micelles no doubt form over a range of concentrations, but the range is sufficiently small that for all practical purposes a precipitous, all-or-none behavior can be assumed. This situation is true for the reactivity-distance relationship. In reference 6, Menger cites several reactions whose rates manifest a severe dependence on distance (i.e., reactions in which a few tenths of an angstrom are worth many orders of magnitude in rate). Extremely fast rates are observed when two functional groups are held within a critical distance. Another particularly striking example is given in the next paragraph. Intramolecular hydride transfer in equation 4 proceeds with an enzyme like E M of 6.5 Χ 10 M . In other words, the intramolecular reaction is 6.5 X 10 times faster than the intermolecular counterpart at 1 M concentration (11). Davis et al. (11) argued that relief of strain cannot explain the fast rate because (a) the equilibrium constant in equation 4 is close to unity and (b) force-field calculations show that hydroxy ketone is only 1.7 kcal/mol more strained than the corresponding dike tone, which lacks nonbonded H / C = 0 interactions. The extremely fast nucleophilic attack on the carbonyl is, however, expected from our "spatiotemporal" hypothesis. Because the mobile hydrogen is held rigidly only 2.35 Â away from the carbonyl carbon, well under the suspected critical distance of 2.8 A (6), the conditions for an enzyme-like acceleration are met. 6

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Why Is It Necessary To Invoke a New Postulate When Intramolecularity Has Already Been Explained by Entropie Factors? The entropie theory of intramolecularity (12) states that nothing is remark able about a nucleophile rapidly attacking an electrophile in the same molecule; this attack is a simple entropie consequence of converting a bimolecular reation into a unimolecular one. Our problems with this view point, given in detail elsewhere (6), consist of the following: (a) Ther modynamics by its very nature cannot describe events on a molecular level. To say that a reaction is fast because of entropie factors is akin to saying that a day is hot because of climatic factors. Both statements may be correct, but neither contains a great deal of information, (b) Entropies of activation (which we have collected from the literature in large numbers) correlate poorly with intramolecular efficiencies. Thus, entropies of activation for reactions in solution can be used neither to rationalize nor to predict; the entropy theory is, in effect, a nontheory. (c) If intramolecular reactions are fast because placing both functionalities in the same molecule is entrophically beneficial, then minor structural variations in the intramolecular system should not impact greatly on the rate. The entropy school incorporates this conclusion into their widely quoted corollary: "Freezing the free rotation about a single bond linking two reactive functionalities improves the intramolecular rate by a factor of only 5". The corollary is illustrated schematically in equation 5. « CH

_ ®

^

ç

®

2

H

CH

ÇH

©

I

^

CH

-(B)

fc = rel

r

2

—

_

φ

^

- ®

5^

CH

0

*

I

Λ

CH

(g)

(5b)

However, in many instances, a single frozen rotation leads to a rate increase of >10 , not 5. A n example is shown below (4). What is the source of this huge discrepancy? 4

O H ^

E M = 4 x 10

4

E M = 5 x 10

8

The entropy theory falters because it does not take into account the prodigious rate effects possible when critical distances are imposed. If two functional groups are connected by a long flexible chain, then inserting a cis double bond in the chain will indeed have only a minor effect on the rate.


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NUCLEOPHILICITY


Residual Soppiness in the chain renders a critical distance unlikely. Although the entropy theory correctly predicts a trivial rate increase in such a system, the system itself is trivial. The really interesting rate increases, some of them reaching enzymatic levels, are not addressed by entropy theory. One final point with regard to comparing the critical-distance and entropy theories is the following. Words like "true and false", "correct and incorrect", and "valid and invalid" have been avoided. Such descriptives have no place in discussions of chemical models that are, above all, fictitious. Models—one must never forget—are to be used, not believed. Thus, I do not claim the spatiotemporal hypothesis represents the "truth"; I merely claim that it is a valuable aid for thinking, especially in cases where entropie arguments fail to help. Can the "Spatiotemporal" Postulate Be Useful in Explaining Nucleophilic Reactivity? This question can be answered affirmatively by citing recent work of Breslow et al. (13), who were interested in the acylation of β-cyclodextrins (CD) by bound esters. When, for example, m-nitrophenyl acetate binds to the β-CD cavity, the ester transfers its àcyl group 64 times faster than it hydrolyzes in water at the same p H : Ο II

Because 64 is not a large acceleration, Breslow et al. began searching for more active substrates. They did this by first constructing molecular models of the tetrahedral intermediate for acylation by a variety of esters. They then assessed the quality of the "fit" within the cavity. This procedure led to the testing of p-nitrophenyl ferrocenylacrylate, a compound whose ferrocene system can enter the cavity and, with a slight tilt, rest its side chain above a β-cyclodextrin hydroxyl:


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Nucleophilicity and Distance 5

The resulting deacylation rate increases to 7.5 Χ 10 times faster than background, an impressive number. Note that the increase from 64 to 7.5 X 10 has nothing to do with the extent of binding because the association constant remains about the same. What in fact were Breslow et al. really doing when they were searching for improved "fits"? In terms of the postu late, they were searching for a substrate that would position its carbonyl at a critical distance from a hydroxyl a high percentage of the time. They suc ceeded in their search and achieved an enzyme-like rate. Although the cyclodextrin-ferrocene association constant is "normal" [in the words of Breslow et al. (13)], the conclusion cannot be made that this association requires little or no energy to attain the critical distance. Something is not gotten for nothing. Very likely the association constant would, in fact, be much larger than "normal" were it not for the enforced proximity of the carbonyl and hydroxyl. When binding energy is sacrificed, the reaction rate is enhanced.


5

What Is the Role of Solvent in the Spatiotemporal Postulate? In reference 6, the critical distance for nucleophilic attack on a carbonyl is estimated roughly as 2.8 Â. This value is less than the diameter of a water molecule. The conclusion is inescapable: the nucleophile and electrophile must desolvate while forming a reactive complex. Once the complex is formed, however, the ensuing reaction can be extremely fast. Indeed, the step in which bonds are formed and broken may not even be rate-determin ing. I can hardly claim this idea is new. In 1952, Glew and Moelwyn-Hughes (14) suggested that the energy necessary to reorganize solvent molecules around reacting species comprises almost all the activation energy of some reactions. Dewar and S torch (15) recently reiterated the concept. The role of solvent is seen particularly clearly in the theoretical work of Chandrasekhar et al. (16) on the S 2 reaction between C l " and C H C 1 . The free energy of activation increases from 3.6 to 26.3 kcal/mol upon passing from the gas phase to water. Note that nowhere in the spatiotemporal postulate is the term "transi tion state" used. This term is not used because the transition state, for reasons just mentioned, is considered peripheral to time and distance. Perhaps the love affair that physical organic chemists are having with "transi tion structure" is overly passionate. Diffusion theory, not quantum mechan ics, may be the key to future progress. N

Is the Ήme-Distance

3

Concept Not Simply a "Strain" Theory?

The answer to this question depends on the definition of "strain". That large rate increases are possible when an intramolecular reaction relieves nonbonded tension elsewhere in the molecule is certainly true. A prime exam ple is given (4):


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NUCLEOPHILICITY

H

COOH E M = 2 x 10

9

CH

3

CH

3

CONHCH3

\COOH

E M = 3 x 10

13


Methyl-methyl interactions are reduced during cyclization of the molecule on the right. This sort of steric acceleration is different from the acceleration induced by holding two functionalities together. In fact, we take great care to avoid reactions where classical steric accelerations muddle the issue. Con sider the following the intramolecular nucleophilic displacements (17):

2 x 10

5

Strain is generated in the cyclizations. Correction for strain effects would only increase the value of 2 X 10 . The extremely fast rate of the azanorbornane derivative must, therefore, be attributed to an enforced residency at bonding distances. Although the time-distance concept is not a traditional strain theory, a similarity exists between the two in that both invoke elevated ground-state energies. This concept requires energy to desolvate a nucleophile and an electrophile prior to holding them at bonding distances. The source of this energy depends on the system. In the azanorbornane derivative, the energy is "covalent" (i.e., imparted to the molecule during its synthesis). Enzymes, on the other hand, sacrifice binding energy to achieve proper geometries. 5

How Is the "Time" Component of the Spatiotemporal Hypothesis Treated? Clearly, for two reactants simply to reach a contact distance is insufficient; they must also retain this disposition. The longer the time that two atoms spend poised in a position to react, the greater the probability of thermal activation and the faster the rate. Because the hypothesis involves, therefore, a pair of fluents (time and distance), we have found it useful to ignore the time by examining only rigid intramolecular systems. Unfortunately, this situation may not always be possible or desirable. In such cases, a "preassociation" constant relating solvent-separated species with van der Waals


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complexes must be evaluated (theoretically or experimentally). Data of this type are not generally available; this situation again leads to my opinion that less emphasis should be given to transition states and more to solution dynamics. Is the Spatiotemporal Postulate Useful in Predicting Chemical Behavior? If the reasonable assumption that the critical distance for nucleophilic attack on an ester (CD ) is larger than that for attack on an amide (CD ) is made, rigid carbon skeletons can then hold a nucleophile and an ester (or corre sponding amide) at a distance D according to three possibilities: (a) D > CO and C D , (b) C D < D < C D , , and (c) D < CO and C D . The kinetic consequences of the different geometries are shown in Table I. By far the most interesting case is the one in which the distance exceeds the needs of the amide but not the ester. In such an event, an intramolecular reaction should be fast only for the ester. Entropy theory, of course, would not make a distinction. In summary, E M values could conceivably vary widely with the nature of the functionalities in chemically similar reactions. I know of no other theory that can make this prediction nor of a study in which the possibility has been systematically tested. And if the spatiotemporal hypoth esis stimulates an experiment, its formulation will have been worthwhile apart from whether the prediction (and others we are now testing) turn out to be correct or not. e

e


e

fl

f l

e

f l

Table I. Kinetic Consequences of Different Geometries. Distance D > CO and CD CD < D < C D D < CO and CD e

fl

fl

e

e

fl

EM of Ester

EM of Amide

small large large

small small large

Acknowledgmen t Support by the National Science Foundation is greatly appreciated. Literature Cited 1. 2. 3. 4. 5. 6. 7.

Bender, M . L . ; Kézdy, F. J.; Gunter, C. R. J. Am. Chem. Soc. 1964, 86, 3714. Hershfield, R.; Schmir, G. L. J. Am. Chem. Soc. 1973, 95, 7539. Parker, A. J. Chem. Rev. 1969, 69, 1. Kirby, A. J. Adv. Phys. Org. Chem. 1980, 17, 183. Menger, F. M . Tetrahedron 1983, 39, 1013. Menger, F. M . Acc. Chem. Res. 1985, 18, 128. Steiger, U. R.; Keizer, J. J. Chem. Phys. 1982, 77, 777.


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8. Cowan, D. O.; Drisko, R. L. Elements of Organic Photochemistry; Plenum: New York, 1976; p 286. 9. Sisido, M . Macromolecules 1971, 4, 737. 10. Pispisa, B.; Palleschi, Α.; Barteri, M . ; Nardini, S. J. Phys. Chem. 1985, 89, 1767. 11. Davis, A. M . ; Page, M . I.; Mason, S. C.; Watt, I. J. Chem. Soc., Chem. Commun. 1984, 1671. 12. Page, M . I.; Jencks, W. P. Proc. Natl, Acad. Sci. U.S.A. 1971, 68, 1678. 13. Breslow, R.; Czarniecki, M . F.; Emert, J.; Hamaguchi, H . J. Am. Chem. Soc. 1980, 102, 762. 14. Glew, D. N.; Moelwyn-Hughes, E. A. Proc. R. Soc. London, Ser. A 1952, 211, 254. 15. Dewar, M . J. S.; Storch, D. M . J. Chem. Soc., Chem. Commun. 1985, 94. 16. Chandrasekhar, J.; Smith, S. F.; Jorgensen, W. L. J. Am. Chem. Soc. 1985, 107, 154. 17. Hutchins, R. O.; Rua, L. J. Org. Chem. 1975, 40, 2567. RECEIVED

for review October 21, 1985.

ACCEPTED

June 17, 1986.


Nucleophilicity and Distance - American Chemical Society

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