Proc. Nat. Acad. Sci. USAVol. 68, No. 8, pp. 1678-1683, August 1971

Entropic Contributions to Rate Accelerations in Enzymic andIntramolecular Reactions and the Chelate Effect

MICHAEL I. PAGE AND WILLIAM P. JENCKS*

Graduate Department of Biochemistry, Brandeis University, Waltham, Massachusetts 02154

Contributed by William P. Jencks, May 20, 1971

ABSTRACT It is pointed out that translational and(overall) rotational motions provide the important entro-pic driving force for enzymic and intramolecular rateaccelerations and the chelate effect; internal rotations andunusually severe orientational requirements are generallyof secondary importance. The loss of translational and(overall) rotational entropy for 2 1 reactions in solutionis ordinarily on the order of 45 entropy units (e.u.) (stan-dard state 1 M, 250C); the translational entropy is muchlarger than 8 e.u. (corresponding to 55 M). Low-frequencymotions in products and transition states, about 17 e.u.for cyclopentadiene dimerization, partially compensatefor this loss, but "effective concentrations" on the orderof 108 M may be accounted for without the introductionof new chemical concepts or terms.

There are several reasons for believing that the specific bind-ing process per se plays an important role in reducing the freeenergy of activation of reactions catalyzed by enzymes. Wewould like to know the nature and magnitude of the maximumincrease in rate that maybe brought about bybringing togethertwo properly oriented reactants in the active site of an enzymewithout invoking strain or desolvation. The rate accelerationin a monomolecular enzymic or intramolecular reactioncompared to a bimolecular reaction may be expressed as an"effective molarity" of one reacting group or molecule relativeto the other. It has been assumed bya number of investigators,including one of us, that this effective molarity is on the orderof 1-55M (up to 8 entropy units), corresponding to the proba-bility of finding solute molecules next to each other, plus arelatively small additional factor reflecting orientational re-quirements of the transition state (1, 2). A similar approach,with "effective concentrations" of 55-110 M, has been pro-posed to explain the chelate effect (3). A recent renewal ofinterest in this subject has prompted the introduction of theterms "rotamer distribution" (4), "orbital steering" (5) and"stereopopulation control" (6) to describe the contribution ofapproximation and, in particular, orientation to intramolecu-lar rate accelerations. The purpose of this communication is topoint out that large "effective concentrations" may be ac-counted for by well-known chemical principles, without theintroduction of new chemical concepts or terms. Althoughthese principles have frequently been discussed with referenceto the problems considered here (3, 7, 8), their application andquantitative significance for reactions in solution do not seemto be generally appreciated.

Large rate accelerations in intramolecular reactions ofrigid, crowded molecules may be caused by steric strain or

desolvation. Unequivocal evidence that theories giving rateaccelerations on the order of 55 AM from entropic factors arewrong or incomplete is provided by several intramolecularreactions, such as ring closures of succinate derivatives, inwhich the presence of one or more free rotations ensures thata reacting group can move out of an unfavorable conformationso that the fraction of the starting material in a high-energy,strained or desolvated form will be negligible. The comparisonbetween intra- and intermolecular reactions may be based onthe free energy of either the transition state, from rate mea-surements, or the product, from equilibrium measurements,relative to the starting material; the latter comparison hasthe advantage that the structure of the product is known.Thus, the equilibrium constant for succinic anhydride forma-tion (Eq. 1) is3 X 105

COOH

GOGH

0

11

=I O11v

(1)

more favorable than that for acetic anhydride formation fromthe free acids, which implies an "effective concentration" of3 X 105 M of the carboxylic acid groups of succinic acid rela-tive to each other (2, 9), and the "effective concentration" ofthe neighboring carboxylate group that determines the rateof anhydride formation from substituted monophenyl succi-nate anions (Eq. 2) is about 105M (4, 10, 11). Such physically

0

C-OR

C-OR-11

0 0

K+ %1C'XI--I +

1100L _ O

-OR

(2)impossible "effective concentrations" correspond to some 23e.u., much larger than 8 e.u. Similarly, the chelate effect forethylenediaminetetraacetate amounts to a factor of 102-4-106.5 compared to two molecules of iminodiacetate, and effectsof comparable magnitude have been reported for other chela-tion equilibria; these large effects were attributed by Schwarz-enbach to a high activity coefficient of a chelating ligandgroup (12).

Reaching the transition state or (monomolecular) productof a bimolecular reaction reduces the number of independent

1678

* To whom reprint requests should be addressed. Publication No.783 of the Graduate Department of Biochemistry.

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Entropic Contributions to Rate Accelerations 1679

species in the system, with a consequent loss of three transla-tional and up to three rotational degrees of freedom. Since thisloss may be avoided if the reactants are bound to the activesite of an enzyme, or by conversion to a first-order intramolecu-lar reaction, the first step in analyzing this problem is to esti-mate the entropy change corresponding to the loss of thesemotions in a 2 -k 1 reaction. Translational and rotationalentropies can be evaluated with considerable confidence boththeoretically and experimentally in the gas phase; some typi-cal values are shown in Table 1. The problem is to evaluatethese quantities for reactions in solution in the face of (a) theabsence of a satisfactory theory of liquids, (b) the difficulty ofseparating translational and rotational modes in the liquidphase (13), (c) the entropy of transfer from the gas to theliquid phase, as indicated by Trouton's rule and its modifica-tions (14, 15), which will influence the entropy of any 2 1reaction, t and (d) the difficulty of directly interpreting experi-mental entropy values in the liquid phase because of solvationeffects.T However, the sum of the translational and (overall)rotational entropies in a liquid phase reaction may be esti-mated as in Eq. 3;Gas A + B = Tx state or Ca

,as lAs= lAs=V-9 4-9 4-15 (3)Solution A + B = Tx state or Cb

a AStrans + rot = -50 to -55 e.u.; AS~b~d(Diels-Alder) = -30to -40 e.u.

ASpredicted = -27 to -37 e.u.; ASobsd = -30 to -40 e.u.

the Diels-Alder dimerization of cyclopentadiene is taken as aconcrete example. The losses of translational and rotationalentropy upon-forming the product (or transition state) of thisreaction, calculated from standard formulas for the partitionfunctions and using the moments of inertia estimated byWassermann (19) are (see Table 1), -31 and -21 e.u., re-spectively, giving a total entropy loss of -52 e.u. in the gasphase and at a standard state of 1 M, 400'K. The differencebetween this value and the observed equilibrium AS valuesbetween -31 and -39 e.u. (20) is a consequence of an un-expectedly large residual entropy from low-frequency internalmotions in the product; the internal entropy of dicyclopenta-diene is 17 e.u. [calculated from the difference between thetotal (21) and the translational plus rotational entropies],which is 11 e.u. larger than the internal entropy of the re-actants (21). Entropy changes for reaching the transition

t This effect may also be expressed in terms of the free volume inthe liquid phase (16). The factor of approximately 150 estimatedfor a free volume of 0.5 ml and a molar volume of 75 ml is equiv-alent to the 10 e.u. (a factor of 150 at 250C) estimated directlyfrom Trouton's rule for reactants and products with similarheats of vaporization (see below).t A further difficulty arises from the fact that thermodynamicactivation parameters for gas-phase reactions usually refer toconstant volume, whereas those for solutions ordinarily refer toconstant pressure. It has been suggested that comparisonsshould be made at constant volume (17, 18), but this requires theuse of liquid-phase data obtained under unusual conditions ofhigh pressure. We believe it is both simpler and more meaningfulto carry out comparisons at constant pressure, for which AHfor a 2 -- 1 reaction in the gas phase differs ideally only by RTfrom that at constant volume. Since this correction is smallrelative to other uncertainties, we have neglected it for presentpurposes.

state are almost identical to those for the overall equilibriumconstant of this and other Diels-Alder reactions (18), and theinternal entropy-of the transition state of some 18 e.u., whichcould be accounted for by 5 low-frequency vibrations near 100cm-I, is similar to that for the reaction product (22). Thelimiting translational plus rotational entropy change of about50 e.u. is equivalent to a factor of 1011 M, but this value cor-responds to a smaller free energy change in the gas phasebecause of the (relatively small) correction for the transla-tional and rotational enthalpy function at 2980K (Table 1).The total entropy change in solution may be estimated

from the entropies of transfer of the reactants to the liquidphase. Although the standard entropy of vaporization ofmany liquids at 1 atm is close to 21 e.u. (14), approximatelyhalf of this quantity is simply the entropy of dilution from apure liquid to a standard state of 1 atm, 10.8 e.u. for a 10 Mliquid. After correction to a common standard state of 1 Mand to 250C, based on the empirical relationship between theboiling point of a liquid and its entropy of vaporization atany temperature (15), the entropy of vaporization of cyclo-pentadiene is 9 e.u. and that of the higher-boiling endo-di-cyclopentadiene is 15 e.u., so that the net change in the entropyof the reaction in the liquid compared to the gas phase is only18 - 15 = 3 e.u. (Eq. 3), similar to the experimental valueof 5 e.u. (23). This is in accord with the well-known experi-mental fact that equilibrium and activation entropies forDiels-Alder reactions of -30 to -40 e.u. are very similar inthe gas and liquid phases (18, 23). We were initially surprisedby this similarity, in view of the widespread assumption thatthere is a .severe restriction to translational and rotationalmotion upon condensation to the liquid phase, but the reasonsfor it are apparent-once the entropy of dilution effect hasbeen allowed for, much (or all) of the remaining expecteddifference of approximately 10 e.u. between the entropies ofvaporization of the reactant and products will ordinarily becompensated by the larger entropy of vaporization of theproduct (or transition state) because of its higher boiling point.It is probable that for most solutes the loss of rotational en-tropy is small upon transfer to the liquid phase, and the ob-served entropy change may be regarded as primarily a loss oftranslational entropy (24). This is in agreement with the factthat there is no significant difference between the entropies ofsolution of noble gases (which have no rotational entropy)and of hydrocarbons of comparable size (25).§We conclude that losses of translational plus rotational

entropy of 40-50 e.u. are to be expected for many bimolecularreactions in solution, in view of the small dependence of thesequantities on molecular size (Table 1), and that this loss willbe compensated to a variable extent by low-frequency motionsin the product or transition state. Thus, the entropic barrierthat must be overcome for a relatively simple reaction havingresidual freedom of internal motions corresponding to about15 e.u., based on a standard state of 1 M, is some -35 e.u.

§ This statement must not be taken too literally in view of thepreviously mentioned difficulty of separating the entropic com-ponents of liquids (13); a more rigorous statement is that uponsolution or condensation of a nonpolar molecule of moderate size,there is little loss of the entropy that is attributable to rotationin the gas phase, although this entropy may be partially con-verted to other modes in the liquid.¶ Estimated from the strain energy of cyclopentane, 7.3 kcal/mol . 5 = 1.4 keal/mol (48).

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1680 1 Chemistry: Page and Jencks

TABLE 1. Typical entropy and free-energy contributions fromtranslations, rotations, and vibrations at 2980K

S0 H0-Ho0 GO-HOO(cal deg1 (koal (kcal

Motion mol-1) molh1) mol-1)

Three degrees of transla-tional freedom for mo-lecular weights 20-200, 29-36 1.48 -7.2 to -9.1standard state 1 M a

Three degrees of rotationalfreedom a

Moments ofinertiab

Water 5.8X 10-120 10.5c 0.89 -2.24n-Propane 5. 0 X 10-116 21. 5c 0.89 -5.53endo-Dicy-

clopenta-diene 3.8 X 10-11' 27.2c 0.89 -7.21

Internal rotations 3-5 0.3' -0. 6 to -1. 2Vibrationsa

W, cm-,

1000 0.1 0.03 0.0800 0.2 0.05 -0.01400 1.0 0.20 -0.10200 2.2 0.35 -0.31100 3.4 0.46 -0.56

a Calculated from standard equations for translation (Sackur-Tetrode equation), rotation (rigid rotator), and vibration (assum-ing a harmonic oscillator) in the gas phase; see for example,Pitzer, K. S., and L. Brewer, Thermodynamics (McGraw-HillBook Co., Inc., New York, 1961).

b Product of three principal moments of inertia, g8 cm6.c Symmetry corrected. d See text.e Typical value; this quantity is a function of the barrier to

rotation and the partition function.

This corresponds to a rate acceleration of 108 M that shouldbe obtainable by binding to an enzyme active site or conver-sion to an intramolecular reaction. The entropy of activationforkthe thermal disrotatory ring closure reaction of Eq. 4,

(.w.

which might be regarded as an intramolecular analog of theDiels-Alder reaction, is -4.7 e.u. in cyclohexane solution(26). The difference between this value and that for bimolecu-lar Diels-Alder reactions, such as cyclopentadiene dimeriza-tion (A&St = -33 e.u.), corresponds to a factor of 106 M at250C favoring the intramolecular reaction.How, then, may these large entropic contributions of -35

to -50 e.u. be reconciled with earlier, smaller estimates forreaction rates and equilibria, including chelation reactions,and with the many observed activation and equilibriumentropies in the range of -8 to -20 e.u. for reactions of me-

dium-size molecules? Either the larger or the smaller valuesmust be "normal" and the other must be "abnormal" or inerror; previously we had believed that the smaller range repre-sented the standard values. Several factors (in addition toexperimental error) may contribute to the difference:

(1) Observed equilibrium entropies of many readily revers-ible association reactions to form hydrogen-bonded or charge-transfer complexes are about -10 to -20 e.u. (27), as ex-pected from naive earlier estimates of the approximation andorientation effects. However, in a typical complex of this sort,(Eq. 5), three degrees of rotational and translational freedom,

0 + R F® . ="cage" "tight" trans-

weak bond sition stateor product

(5)

corresponding to some 45 e.u., have been converted into a low-frequency stretching vibration, an internal rotation, and fourlow-frequency bending modes which must contribute up to 30e.u. of residual entropy to the loose complex. An unhinderedinternal rotation will contribute roughly 7 e.u.; low-frequencystretching, deformation, and torsional motions involvingthe hydrogen or charge-transfer bond, in the range of 50-300cm-, (28) account for the remainder of the difference. Simi-larly, the low-frequency vibrations of metal-ligand bonds andother motions (29) make a significant contribution to theinternal entropy of chelate complexes, and a comparablesituation exists for the freezing of an organic compound into acrystal lattice-the entropy of fusion of only some -10 e.u.that is observed for many organic molecules (30, 31) may beregarded as a result of the replacement of translationaland rotational degrees of freedom by low-frequency motionswithin the lattice (32). For example, it has been estimatedthat in crystalline hexamethylenetetramine the "transla-tional" frequency of 73 cm-' and torsional frequency of 45cm-' contribute 14.2 and 15.1 e.u., respectively, to theentropy at 2985K (32).

(2) Differences in the solvation of polar and hydrophobicgroups of reactants, transition states, and products are likelyto make large and unpredictable contributions to observedSquilibrium and activation entropies, especially in aqueoussolution. Thus, the equilibrium entropies for reaction 6 rangefrom -5.4 to -28 e.u. for the addition of semicarbazide,hydrogen cyanide, amides, water, and hydrogen peroxide to

XH + CO= X-C-OH/, ~~~~~~~~~~~~~~~~~~~I

(6)

the carbonyl group (33, 34). The reduction of ketones bymorpholine-borane, with AS* = -40 e.u., provides a goodexample of a reaction with a large negative entropy that isalmost solvent-independent and therefore is probably notseriously perturbed by salvation effects (35).

INTERNAL ROTATIONS

We believe that the contributions of internal rotations orhigh degrees of orientational restriction to entropies of activa-tion and reaction or to rate accelerations in systems in whichthese rotations are initially frozen are generally small. It haspreviously been pointed out that very severe orientationalrequirements would require force constants in a transitionstate larger than those for a covalent bond (36), and it may benoted further that the fact that some intramolecular reactionsare slower than others because of unfavorable geometry andsteric effects does not necessarily imply a high orientationalrequirement for either intermolecular or intramolecular reac-tions. No more entropy can be lost upon freezing a rotation

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Entropic Contributions to Rate Accelerations 1681

than was present in the rotation initially. Entropies of internalrotation in the gas phase are known experimentally and are ingood agreement with theory (37); they will not be larger insolution. Some representative examples, based on a series ofring closures, are shown in Table 2. The entropy changes areprimarily a consequence of losses of internal rotation that maybe partially compensated by low-frequency motions in thecyclic products; contributions from changes in overall rota-tional entropy, symmetry, other internal vibrations, andlosses of two hydrogen atoms upon cyclization are relativelysmall and will be neglected for present purposes. The entropyloss per internal rotation for saturated hydrocarbons of up to8 carbon atoms is 2.7-4.3 e.u.; after correction for low-fre-quenicy motions in the C4, C5, C7, and C8 rings, the entropyloss, AScorr, is 3.7-4.9 e.u. per internal rotation. Entropies ofactivation for ring closure reactions are similar or smaller(Table 2), so that we may take 4.5 e.u. as a representativevalue for the entropy that may be lost upon freezing an inter-nal rotation, in the absence of compensating factors. Thisvalue, which is in good agreement with the calculated value(37), is less than the maximum that would be expected forfree rotation because of the entropy loss resulting from thebarrier to free rotation in saturated hydrocarbons (38). Oneimportant consequence of this barrier is that the loss of ro-

tational entropy upon ring closure of a system containing a

double bond is not significantly different from that of a

saturated system which initially has one more internal rota-tion (Table 2). This is a consequence of the reduced barrier torotation adjacent to the double bond and of changes in thesymmetry axis in the acyclic compound (39) and brings intoquestion the common assumption that ring-closure reactionsof unsaturated systems are favorable entropically comparedto those of saturated systems.

It should be noted that the entropy of an internal rotationis almost completely lost upon the imposition of a relativelysmall orientational restriction (e.g., an 80% loss upon con-

version of a free internal rotation, corresponding to 7 e.u., to a

vibrational frequency of 300 cm-'), and no significant furtherloss occurs with very high degrees of orientational restriction.Even the complete freezing of a free internal rotation with theloss of 7 e.u. corresponds to a factor of 34 which, based on

360° of rotation in one plane, gives a maximum degree of"orbital steering" of only 11° that can be attributed to loss ofentropy. Finally, the loss of entropy upon freezing an internalrotation is partially compensated by a favorable enthalpyfunction change of about 0.5 kcal/mol, so that the increases infree energy from the loss of each internal rotation in the for-ination of 4-, 5-, and 6-membered rings are 0.99, 0.90, and0.76 kcal/mol, respectively, corresponding to a rate factor ofabout at 25"C. The relative importance of different entropiccontributions is well illustrated by the dimerization of 2-propene to cyclohexane, for which the overall entropy lossof 50.1 e.u. (30) is composed of 48.7 e.u. from translationaland overall rotational entropy (39) and only 1.4 e.u. frominternal entropy, which includes the loss of two internal rota-tions (5.8 e.u.) and a compensating increase from internalvibrations (9.2 - 4.8 = 4.4 e.u.) (40).This rate factor of 5 is considerably smaller than the factor

of 230 which has been suggested for the freezing of each in-ternal rotation and which led to the suggestion that favorable"rotamer distribution" is a factor of prime importance inintramolecular and enzymic rate accelerations (4, 36). The

value of 230 is based on comparisons of rates of ring closure of

TABLE 2. Entropy changes accompanying cyclization at 2980K

System"

.A

\v\/ *k"

VA

\AA/

VW\

- ASO(cal deg-'molh')

7.7

Aso/(no.

int.

rot.)

3.85

- AScorr/(no.int.

rot.)

3.85

7.0 7.00

10.9 3.63 4.90

10.3 5.14

13.3 3.32 4.77

13.1 4.37

21.2 4.25 4.25

21.0 5.25

19.8 3.30 3.72

19.6 3.92

19.0 2.71 3.91

18.8 3.13

Astcal.deg-' - ASt/(no.

Transition state mole-' int.rot.)

6-memberedClaisen rearrangements -2 to -14 0.7 to 4.7Cope rearrangementc -8 to -12 2.7 to 4.0Ester pyrolysesd +4 to -8 -1.3 to 2.7hexatriene -- 3-cyclohexadienee -4.9 2.45

(4000K)5-memberedCH3CH2NO2 C2H4 + HNO2f -9 4.5

4-memberedElimination of HX from alkyl

halidesd +5 to -3 -5 to 3

a Data from ref. 21, 30; O'Neal, H. E., and S. W. Benson, J.Chem. Eng. Data, 15, 266 (1970).

b Goering, H., and R. R. Jacobson, J. Amer. Chem. Soc. 80, 3277(1958); White, W. N., and C. D. Slater, J. Org. Chem., 27, 2908(1962).

v Foster, E. G., A. C. Cope and F. Daniels, J. Amer. Chem. Soc.,69, 1893 (1947).

d Ref. 47.e Lewis, K. E., and H. Steiner, J. Chem. Soc., 3080 (1964).f Fr6jacques, M. C., C. R. Hebd. Acad. Sci. (Paris), 231, 1061

(1950).

different-sized ring systems in acyl-transfer reactions, but isby no means general. For example, although the ring closureof phenyl succinates is about 200 times faster than that ofphenyl glutarates, the relative rates of ring closure of other5-membered ring systems, including other acyl-transfer reac-

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1682 Chemistry: Page and Jencks

tions (41), are essentially the same or even smaller comparedto those of the corresponding 6-membered systems (42).These differences reflect the specific geometric and electronicrequirements for the transition states of these different reac-tions, so that no generalization as to the magnitude of thecontribution of "rotamer distribution" can be made from thiskind of data. For example, the transition state for the phenylglutarate reaction contains an Sp2 carbon atom in the acy]group, which is known to destabilize 6-membered rings (43),and the transition state for the phenyl succinate reaction maygain some 3-4 e.u. from the low-frequency puckering motioncharacteristic of 5-membered rings (44). The relatively slowrate of closure of 6-membered rings in certain SN2 displace-ment reactions (45) presumably reflects the unfavorablegeometry brought about by a 900 bond angle, which is alsolargely responsible for the relative instability of most 6-membered compared to 5-membered chelate rings (46). Thelargest total loss of entropy from internal rotations that islikely to be encountered is about 20 e.u. for the closure of anunsubstituted 6-membered ring, which Westheimer andIngraham (8) have pointed out is enough to offset most of thecontribution of translational entropy to the chelate effect(estimated from gas-phase values), but even this value shouldbe reduced by the contribution of low-frequency motions in-volving the metal-ligand bond to the internal entropy of thechelate complex.The observed "effective concentration" of about 105 M in

succinate reactions may be corrected for the loss of three in-ternal rotations upon ring closure to provide an estimate of themaximal rate acceleration that may be expected for an enzy-mic acyl-transfer reaction as a consequence of optimal bindingof substrates, without strain or desolvation. Allowing 0.9kcal/mol for the rotation around the methylene-methylenebond and 1.8 kcal/mol for each free rotation about the methyl-ene-carboxyl residue bond (47) to give a rate factor of 103 andan additional factor of 10 for eclipsing of the methylene hydro-gen atoms in the 5-membered succinate ring¶ the total"effective molarity" is 109 M, which may be compared to thevalue of 108 M cited above. This supports the conclusion thatthe similar factor that has been directly observed for a rigidbicyclic analog of phenyl succinate may be accounted forwithout invoking strain or desolvation (4, 11). It further sug-gests that the observed entropy of activation of many acyl-transfer reactions involving uncharged reactants, which isoften on the order of -30 to -50 e.u. and is usually attributedto orientation of solvent (49), may be in large part a conse-quence of the loss of translational and rotational entropy inthe relatively tight transition state that is made possible bythe availability of orbitals from the unsaturated carbonylgroup in such reactions.

In conclusion, we suggest that the contributions of transla-tional and (overall) rotational entropy to reaction rates andequilibria in solution are larger than has generally been be-lieved and support the view that enzymes can carry out alarge fraction of their extraordinary rate accelerations byvirtue of their ability to utilize substrate-binding forces toact as an "entropy trap" (50). It follows from this conclusionthat low-energy conformational changes that are possiblewithin the enzyme-substrate complex are disadvantageouswith respect to the contribution of this entropy effect to thecatalytic process, as they are also for the utilization of strain

We are grateful to Drs. B. Capon, T. C. Bruice, and J. 0.

Edwards for communication of manuscripts before publication.This work was supported by grants from the National ScienceFoundation (GB 5648) and the National Institute of ChildHealth and Human Development of the National Institutes ofHealth (HD 01247).

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2. Jencks, W. P., Catalysis in Chemistry and Enzymology(McGraw-Hill, New York, 1969), chap. 1.

3. Schwarzenbach, G., Helv. Chim. Acta, 35, 2344 (1952);Adamson, A. W., J. Amer. Chem. Soc., 76, 1578 (1954);Martell, A. E., in Essays in Coordination Chemistry, ed. W.Schneider, G. Anderegg, and R. Gutt (Birkhauser, Basel,1964), p. 52.

4. Bruice, T. C., and U. K. Pandit, J. Amer. Chem. Soc., 82,5858 (1960); Proc. Nat. Acad. Sci. USA, 46, 402 (1960).

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6. Milstien, S., and L. A. Cohen, Proc. Nat. Acad. Sci. USA,67, 1143 (1970).

7. Capon, B., Essays in Biochemistry (Academic Press, London,1971), Vol. 7, in press; Jaff6, H. H., J. Amer. Chem. Soc.,79, 2373 (1957).

8. Westheimer, F. H., and L. L. Ingraham, J. Phys. Chem., 60,1668 (1956).

9. Jencks, W. P., F. Barley, R. Barnett, and M. Gilchrist,J. Amer. Chem. Soc., 88, 4464 (1966); Higuchi, T., L.Eberson, and J. D. McRae, J. Amer. Chem. Soc., 89, 3001(1967).

10. Bender, M. L., and M. C. Neveu, J. Amer. Chem. Soc., 80,5388 (1958); Gaetjens, E., and H. Morawetz, J. Amer.Chem. Soc., 82, 5328 (1960).

11. Bruice, T. C., and A. Turner, J. Amer. Chem. Soc., 92, 3422(1970); Bruice, T. C., in The Enzymes, Vol. II, ed. P. D.Boyer, H. Lardy, and K. Myrback (Academic Press, NewYork, 1970), 3rd ed., p. 217.

12. Schwarzenbach, G., Chemical Specificity in Biological Inter-actions, ed. F. R. N. Gurd (Academic Press, New York,1954), p. 164; Irving, H., R. J. P. Williams, D. J. Ferrett,and A. E. Williams, J. Chem. Soc., 3494 (1954).

13. Ewing, G. E., Accounts Chem. Res., 2, 168 (1969).14. Trouton, F., Phil. Mag., 18, 54 (1884); Hildebrand, J. H.,

J. Amer. Chem. Soc., 37, 970 (1915); 40, 45 (1918); J.Chem. Phys., 7, 233 (1939); Pitzer, K. S., J. Chem. Phys., 7,583 (1939); Everett, D. H., J. Chem. Soc., 2566 (1960).

15. Hildebrand, J. H., and R. L. Scott, Solubility of Nonelectro-lytes (Reinhold Publ. Corp., New York, 1950), 3rd ed., p.427.

16. Frost, A. A., and R. G. Pearson, Kinetics and Mechanism(John Wiley & Sons, 1961), 2nd ed., p. 123.

17. Newitt, D. M., and A. Wassermann, J. Chem. Soc., 735(1940); Moelwyn-Hughes, E. A., The Kinetics of Reactionsin Solution (Oxford Univ. Press, 1947), p. 351.

18. Wassermann, A., Diels-Alder Reactions (Elsevier Publ. Co.,Amsterdam, 1965).

19. Wassermann, A., Proc. Roy. Soc. Ser. A, 178, 370 (1941).20. Herndon, W. C., C. R. Grayson, and J. M. Manion, J. Org.

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