J . Phys. Chem. 1986, 90,411-471 any gas-phase steps support the recent suggestionsl1J2that the source of the space shuttle glow may be NO2*. This emission was first discovered in photographs taken during the third and fourth space shuttle missions (STS-3 and STS-4) while the vehicle was on the night side of the earth.37*38An orangish glow initially thick and later revised to 20 cm estimated to be 5 to 10 cm37*38 thickI2 was observed adjacent to the windward side of the vehicle. This glow is the result of an interaction between the spacecraft and the surrounding atmosphere. At the very low pressures in the vicinity of 240 km where the shuttle glow has been observed, the emission of light must be due to an excited molecule formed (37) Banks, P. M.; Williamson, P. R.; Raitt, W. J. Geophys. Res. Lett. 1983. 10. 118.
(38) Mende, S.B.; Garriott, 0.K.; Banks, P. M. Geophys. Res. Lett. 1983, 10, 122.
(39) The diffusion coefficient of electronically excited NO2 may be different from that for ground-state NOz. The value of 0.1 1 is selected as a value typical of triatomics in air.
471
on the surface, escaping from the surface, and then emitting light. Any subsequent reaction in the gas phase can be neglected as a result of the long mean free path. The formation of 02(A3&+) above a nickel catalyst in an 0-atom stream formed by an ac glow discharge through molecular oxygen is proposed to also have two mechanisms contributing to the formation of the observed electronically excited state. The observed effective lifetime, as measured by the decrease in intensity as a function of distance from the catalyst surface, increases with increasing 0-atom concentration. Since the 02(A32,+) state is known to be quenched strongly by 0 atoms this suggests a mechanism involving two pathways for 02(A3Z,+) formation, one of which involves a longer-lived precursor. Acknowledgment. The authors thank Rensselaer Polytechnic Institute for support of this work. Registry NO.NO, 10102-43-9; 0,17778-80-2; N02, 10102-44-0; 0 2 , 7782-44-7; Ni, 7440-02-0.
Structure and Reactivity in Ionic Reactions Chau-Chung Han, James A. Dodd, and John I. Braurnan* Department of Chemistry, Stanford University, Stanford, California 94305 (Received: July 22, 1985)
Rates and mechanisms of selected bimolecular nucleophilic substitution and proton-transfer reactions involving anionic reactants in both the gas and solution phases are summarized and compared. The predictive power of various rate-equilibrium relationship, especially Marcus theory, is discussed. The nucleophilic reactivity (A&*) is found to correlate better with the nucleophile methyl cation affinity (MCA) than with basicity. The effect of solvent on Hammett p values observed for methyl transfer reactions is considered.
I. Introduction Ionic reactions play a central role in chemistry. For instance, many of the most powerful synthetic reactions utilize ionic reagents. The ability to make modest changes in reaction conditions, such as solvent, leaving group, or counterion, enables one to manipulate rates and chemical products with extraordinary control. Nevertheless, our true understanding remains limited; the delineation of conditions that optimize the yield of a desired product is a process that relies on experience-patterns found in previous studies-rather than on some theoretical footing. Useful predictive tools would find application to chemical reactions taking place in different physical environments. We have been pursuing experiments in the gas phase, where organic systems can display "intrinsic" reactivity in the absence of solvent molecules. The rate of a particular reaction is in general much different in solution than in the gas phase; indeed, the effect of including even one or two solvent molecules into the reaction system can be dramatic, especially for acid-base reactions.' Comparison of the solution- and gas-phase rates can often provide valuable information. In principle, a complete quantum mechanical description of a reaction-one that could describe the potential surface and the dynamics that take place on it-would allow prediction of all aspects of its chemistry. Unfortunately, an accurate potential surface for a complex polyatomic system is quite difficult to obtain, and even if one did possess an accurate surface, the best that could
be said for any subsequent dynamical analysis is that it would be far from routine. The alternative is to make use of the empirical and semiempirical theories that have historically furnished much of the predictive power in describing chemical reactions. Additivity methods that are used to calculate such quantities as heats of formation and molecular polarizability are well established and in widespread use. The predictions afforded by linear free energy relationships have provided many insights over the years. Indeed, many semiempirical rate-quilibrium equations have been applied with equal effect to reactions in the condensed and gas phases. One might conceivably criticize one or more of these theories for their apparent lack of sensitivity to gross environmental changes; nevertheless, their great predictive success-especially that of Marcus theory-makes for a strong rebuttal. There is no doubt that the effects of solvent are considerable, but these effects can be taken account of in uncovering basic similarities in solutionand gas-phase chemistry. The focus in this paper is on two of the simplest ionic reactions: proton transfer and nucleophilic substitution. We first discuss our approach to the study of gas-phase reactivity. We then retreat a bit to consider the history of rate-equilibrium relationships, as well as the more recent Marcus (and related) theories. The next section presents some examples of predictions that are made possible through the semiempirical theories, followed by a discussion of relevant empirical correlations. We conclude with a brief consideration of ionic reactions in solution.
(1) (a) Bohme, D. K. NATO Adu. Sci. Int. Ser., Ser. C 1984, 118, 111. (b) Moylan, C. R.; Brauman, J. I. Annu. Rev. Phys. Chem. 1983, 34, 187.
11. An Approach to the Study of Ion-Molecule Reactions The rate of a gas-phase ion-molecule reaction is determined by both the collision rate and the efficiency with which the collision complex is converted into products. Because of the characteristic long-range ion-induced and -permanent dipole interactions, a
(c) Reaction mechanisms may also change on proceeding from the gas phase to solution. For instance, see: Caldwell, G.; Rozeboom, M. D.; Kiplinger,
J. P.; Bartmess, J. E. J . Am. Chem. SOC.1984, 106, 809, and references therein.
0022-3654/86/2090-0471$01.50/0
0 1986 American Chemical Society
412
The Journal of Physical Chemistry, Vol. 90, No. 3, 1986 A
B
A
k2.
k-I
k-2
7
h3. i
k -3
Figure 1. Double minimum potential energy surface characteristic of many gas-phase ion-molecule reactions.
hard-sphere collision model is not appropriate for estimating the collision rates. Two models which take these forces into consideration are most frequently used for this purpose: the Langevinh and the average dipole (ADO) theories. Many exothermic ion-molecule reactions are unit efficient (they occur on every collision); for these reactions the theories predict a reaction rate that is usually in good agreement with experiment.2e When chemistry becomes important, however, reactions can be slowed down and the calculated collision frequencies serve only as an upper limit. Just as for reactions in solution, the most obvious cause of a slow reaction in the gas phase is an energy barrier along the reaction coordinate. Although a simple barrier cannot explain the frequently observed negative temperature dependence3of these slow reaction rates, a double minimum potential surface4 (such as shown in Figure 1) explains the kinetics, at least qualitatively, and indeed has been shown to be generally correct. The secondary energy barrier (labeled AE* in Figure 1) retards the reaction for entropic as well as energetic reasons. At the orbiting transition state of the collision process, labeled A in Figure 1, the ionic and molecular fragments are separated4 by about 5-10 A. This transition state is characterized as “loose”, since at this separation both the ionic and neutral fragments of the reacting pair can retain their external rotational degrees of freedom. At transition state B, the separation between the colliding pair decreases to the extent that orbital overlap between the two fragments is substantial. At this “tight” transition state, atom or group transfer occurs in proton transfer and SN2reactions. The external rotational degrees of freedom originally present in the reactants and transition state A will be either seriously hindered or totally frozen, and are replaced by bending and symmetric stretching vibrations. While these new vibrations usually have quite low cm-I), they cannot make up for the loss f r e q ~ e n c i e s(100-400 ~-~ in entropy incurred by the removal of external rotational degrees of freedom. Therefore, in terms of statistical reaction rate theory, transition state B has many fewer states available at a given total energy than transition state A. This unfavorable constraint slows an ion-molecule reaction even though the transition state may be energetically lower than the reactants. (The central barrier may also be higher in energy than the reactants. Under hightemperature and high-pressure conditions, one can observe reactions for such systems.6) A general feature of the potential surface presented above is t h a t t h e r e a c t a n t s are highest in e n e r g y along t h e reaction co(2) (a) Langevin, P. M. Ann. Chim. Phys. 1905, 5 , 245. (b) Bowers, M. T.; Laudenslager, J. B. J . Chem. Phys. 1972, 56, 4771. (c) Su,T.; Bowers, M. T. Int. J . Moss Spectrom. Ion Phys. 1973, 12, 341. (d) Su,T.; Bowers, M. T. J. Am. Chem. SOC.1973,95, 1370. (e) For a review of collision theories see Su,T.; Bowers, M. T. In “Gas Phase Ion Chemistry”, Bowers, M. T., Ed.; Academic Press: New York, 1979; Vol. I . (3) (a) Meot-Ner, M. In ‘Gas Phase Ion Chemistry“, Bowers, M. T., Ed.; Academic Press: New York, 1979; Vol. 1. (b) Sen Sharma, D. K.; Kebarle, P. J . Am. Chem. SOC.1982, 104, 19. (4) (a) Pellerite, M. J.; Brauman, J. I. J. Am. Chem. SOC.1980,102, 5993. (b) Olmstead, W. N.; Brauman, J. I. J. Am. Chem. SOC.1977, 99, 4219. (c) Farneth, W. E.; Brauman, J. I. J . Am. Chem. SOC.1976, 98, 7891. (5) Pellerite, M. J.; Brauman, J. I. J . Am. Chem. SOC.1983, 105, 2672. (6) Caldwell, G.; Magnera, T. F.; Kebarle, P. J . Am. Chem. SOC.1984, 106, 959.
Han et al. ordinate; thus both the intermediates (labeled CRand Cpin Figure 1) are chemically activated under the low-pressure conditions characteristic of many mass spectrometers. For such chemically activated species, statistical theories like phase space theory7 and RRKM theorys have been widely and successfully applied in interpreting observations of gas-phase ion-molecule reactions. In our laboratory we have used RRKM theory to extract the central energy barrier, AE* in Figure 1, from experimental data! Under the assumptions that the ion-molecule collision complex CR is sufficiently long lived so that the energy is randomized among all the internal modes of the complex, and that all of the microscopic pathways to products are equally probable, RRKM theory allows the estimation of the energy difference between transition states A and B (Edif= E, - AE* in Figure 1) from the experimental efficiency (eq 1). In this equation, kobsdis the
experimental second-order rate constant, and k, is the ion-molecule collision rate constant calculated from ADO theory. The other rate constants are defined in Figure 1. In the case of an identity reaction (k-l = k3, k2 = k-2) or a reasonably exothermic reaction ((k-] + k&k3 >> k-2k-1), eq 1 simplifies to k,/(k-l + 2k2) and k 2 / ( k I k2), respectively. If the well depth Ew of the ionmolecule complex CR is known, one can calculate the height AE* of the central energy barrier. These energies can be analyzed in terms of rate-equilibrium relationships, and also through Marcus theory, yielding valuable clues as to reactivity in organic ionmolecule reactions.
+
111. Rate-Equilibrium Relationships The approach to chemical reactivity using rate-equilibrium relationships has its origins in the study of proton transfer in solution. The experimental work of Bronsted and Pedersen9 led them to propose that an empirical relationship exists that connects the reaction rate for proton transfer with a pertinent equilibrium constant. According to the Bronsted model, if one varies the catalyzing acid strength by using structurally similar acids with different acidity constants K,, the rate constants k for the proton-transfer step should also vary in a predictable way (eq 2). a d l n k = a d l n K, (2)
is the slope of the empirical relationship and has some significance as explained below. A similar equation can be written for reactions catalyzed by a base. The scope of application of linear free energy relationships was augmented in subsequent years by developments in two directions. Hammett and co-workersI0 generalized such correlations beyond proton-transfer reactions by introducing a standard reference reaction, the ionization of benzoic acids in water. The other development was conceptual. Following the introduction of transition state theory,” Be11I2 and Evans and Polanyi13 showed that the Bronsted equation could be recast in terms of energies; in eq 3, AE* is the activation energy and AEo is the overall energy dAE* = a dAEo
(3)
of reaction. Equation 3 implies that a small variation in AEO results in a corresponding variation in AE*, with constant of proportionality a. Suppose AEo becomes large and positive, as in the case of a very endothermic reaction. The Hammond postulate14 suggests (7) (a) Chesnavich, W.J.; Bowers, M. T. Chem. Phys. 1977,66,2306. (b) Chesnavich, W. J.; Bowers, M. T. Chem. Phys. Lett. 1977, 52, 17. (8) (a) Forst, W. “Theory of Unimolecular Reactions”; Academic Press: New York, 1973. (b) Robinson, P. J.; Holbrook, K. A. “Unimolecular Reactions”; Wiley-Interscience: New York, 1972. (9) Bronsted, J. N.; Pedersen, K. 2.Phys. Chem. 1924, 108, 185. (10) Hammett, L. P. ‘Physical Organic Chemistry”; McGraw-Hill: New York. 1940. (11) Eyring, H. J . Chem. Phys. 1935, 3, 107. (12) Bell, R. P. Proc. R . SOC.London, Sec. A 1936, A154, 414. (1 3 ) Evans, M. G.; Polanyi, M. Trans. Faraday SOC.1938, 34, 11. (14) Hammond, G. S. J . Am. Chem. SOC.1955, 77, 334.
The Journal of Physical Chemistry, Vol. 90, No. 3, 1986 413
Structure and Reactivity in Ionic Reactions 1 -
AEO
-
piax/
+lG*l
0
AEO
Figure 2. Marcus a as a function of reaction energy change. a can take on values between 0 and 1 and is a linear function of AEO between the extremes of flAE’,,,I, where IAEo,,,I = 4AE0*.
that the transition state for such a reaction should resemble the products structurally, and that it should be of similar energy. Consequently, AE* AEO. This situation further implies that a 1, since a change in AEO will produce the same change in AE*. Conversely, if AEO becomes large and negative, as in the case of very exothermic process, the transition state resembles the reactants and AE* 0. This implies that a 0, since a change in AEo will not alter AE* much; it remains about zero regardless of any minor perturbation of the overall thermochemistry. Thus, one might expect a to take on values between 0 and 1 and to reflect in some way the exothermicity of the reaction, as illustrated schematically in Figure 2 . The above reasoning leads to an interpretation of a known as the Leffler postulate,I5 namely, that a is a measure of the position of the transition state along the reaction coordinate. This interpretation has proven to be useful; for instance, in the case of general catalysis, the value of the observed a depends on the nature of the proton-transfer step. The quantitative understanding of rateequilibrium relationships was greatly enhanced with the advent of a theory developed by Marcus16 and by Levich and Dogonadze.17 Marcus derived eq 4 using electron transfer in solution as a model reaction. AE*
-
-
-
+
AE* = (AEo)2 AEo* 16AEo*
+ ‘/,AEo
(4)
and AEo are defined as before; AEo* is the “intrinsic” activation barrier that would exist in the absence of any thermodynamic driving force, i.e. when AEO = 0. It may be thought of as the purely kinetic contribution to the reaction barrier. The generality of eq 4 to chemical reactions has only more recently become apparent. It has been shown, for instance, that the equation can be derived through a number of different approaches that in many cases make only general assumptions about reactivity that would be easily satisfied in many systems.l* In addition, a purely geometrical derivation that models the reaction coordinate as intersecting parabolas results in the same formula.19 An important consequence of the Marcus equation is that it provides an expression for a. Differentiating eq 4 with respect to AEo at a constant AEo* yields 5. This expression quantifies dAE* - - a = - AEo + A (5) dAEo 8AEo* 2 the above discussion concerning the variation of a and shows that (15) (a) Leffler, J. E.; Grunwald, E. ‘Rates and Equilibria and Organic Reactions”; Wiley: New York, 1963. (b) Leffler, J. E. Science 1953, 117, 340. (16) Marcus, R. A. Annu. Rev. Phys. Chem. 1965, 15, 155. (17) (a) Levich, V. G. Ado. Elecfrochem.Electrochem. Eng. 1966, 4, 249. (b) Dogonadze, R. R. In “Reactions of Molecules at Electrodes”, Hush, N. S., Ed.; Wiley: London, 1971; p 135. (18) Murdoch, J. R. J . Am. Chem. SOC.1972, 94, 4410. (19) McLennan, D. J . J . Chem. Ed. 1976, 53, 348.
Figure 3. Variation of reaction energy barrier as a function of reaction energy change as predicted by eq 4. For a thermoneutral process the energy barrier is the intrinsic barrier AEo*. CY is indeed not a constant-as in the case of a linear free energy relationship over a small range of AEO-but that in general it must vary with A E O , as shown in Figure 2. In Figure 3, AE* is plotted against AEo according to eq 4. The slope, which is a,varies from 0 to (where AEO = 0) to 1. Marcus has asserted that a condition for obtaining a linear free energy correlation is that AEo* be constant for the series of reactions under study.20 Reactions with the same AEo* lie on the same AE* vs. AEO curve; if, in addition to this, the reactions span a relatively small range of A E O , a linear free energy relationship will be obtained. Perhaps even more striking than the facility with which the Marcus equation can be derived is its success in predicting the rates of ionic reactions, both in the gas phase and in solution. In addition to solution-phase electron-transfer reactions, solutionand gas-phase atom and proton transfer,20*21a,b and methyl group t r a n ~ f e r ~reactions ? ~ ~ ~ *have ~ been found to be well modeled through Marcus theory. The application of Marcus theory to methyl group transfer has been fruitful in recent years. The analysis has been used to obtain intrinsic barriers for gas-phase SN2 reaction^.^^^^ In addition, the concepts of nucleophilicity and leaving group ability have been shown to be equivalent in the context of the SN2 identity reaction X- CH3X XCH3 X-. The finding that the intrinsic barriers can be correlated with the methyl cation affinity of X- represents an empirical correlation that will be discussed below. Other workers have provided insight at a more detailed level into the workings of Marcus theory as it applies to methyl transfer reactions in solution (vide infra).21cThe application of Marcus theory to SN2 reactions has proven to be remarkably interesting; the theory has obviously moved well beyond its original conceptual limits. It should be noted here that other such “nonlinear” free energy relationships have been developed with the aim of better quantifying or generalizing the Marcus approach.23 The various equations usually predict barriers that are in close agreement with Marcus equation predictions, and thus operationally prove little different from the basic eq 4. Since the Marcus theory precedes the others, and since it has been the most often applied to the interpretation of experiment, it will be focused on. The discussion here by no means lessens the value or efficacy of other free energy relationships, which should prove to be of help as experimental
+
-
+
(20) Cohen, A. 0.;Marcus, R. A. J . Phys. Chem. 1968, 72, 4249. (21) (a) Albery, W. J. Annu. Rev.Phys. Chem. 1980,31,227. (b) Kresge, A. J. Acc~Chem. Res. 1975,8, 354. (c) Albery, W. J.; Kreevoy, M. M. Adv. Phys. Org. Chem. 1978, 16, 87. (d) Lewis, E. S.; Hu, D.D.J . Am. Chem. SOC.1984, 108, 3292. (22) Barfknecht, A. T.; Dodd, J. A.; Salomon, K. E.: Tumas, W.; Brauman, J . I. Pure Appl. Chem. 1984,56, 1809. (23) See Murdoch, J. R. J . A m . Chem. SOC.1983, 105, 2159, for a comparison of these relationships, some of which are detailed in the following: (a) Agmon, N . ; Levine, R. D. J . Chem. Phys. 1979, 71, 3034. (b) Kurz, J. L. Chem. Phys. Lett. 1978, 57, 243. (c) le Noble, W. J.; Miller, A. R.; Hamann, S. D. J . Org. Chem. 1977,42, 338. (d) Thornton, E. R. J . Am. Chem. SOC. 1967, 89, 2915. (e) Rehm, D.; Weller, A. Isr. J . Chem. 1970, 8, 259. (f) Zavitsas, A. A.; Melikian, A. A. J . Am. Chem. SOC.1975, 97, 2757. (g) Johnston, H. S.; Parr, C. J . Am. Chem. SOC.1963, 85, 2544. (h) Ahrland, S.; Chatt, J.; Davies, N . R.; Williams, A. A. J . Chem. SOC.1958, 276. (i) Lewis, E. S.;Shen, C. C.; More O’Ferrall, R. A. J. Chem. SOC.Perkin Trans. 2 1981, 1084. u) Bell, R. P. J. Chem. SOC., Faraday Trans. 2 1976, 72,2088.
414
Han et al.
The Journal of Physical Chemistry, Vol. 90, No. 3, 1986
results appear that provide more exacting tests of the theory. IV. Predictions As discussed above, one would expect that, over a wide enough range of AEO, AE* would not remain linear with A E O , but that the slope a would tend toward 0 for very exothermic reactions and toward 1 for very endothermic reactions. Thus, in general, one would expect to obtain curvature in a Bronsted-type plot of AE* vs. AEO, unless the range of AEO is small. Actually, given the Marcus expression (eq 4) and a single experimental or calculated value of AE* at a known AEO, the entire AE* vs. AEO curve can be constructed for a constant Bo*. Rates for similar processes can be predicted from the known rate of one reaction, in contrast to a Bronsted-type correlation in which additional reaction rates can be predicted given a group of reactions for which the rates are known. Cohen and Marcus used these ideas for a modeling study of small group transfer reactions (proton and atom) that provided fundamental support for the greater generality of the Marcus equation.20 The activation barrier for a transfer reaction which is at or near thermoneutrality is the intrinsic barrier AEo*. Using this value and eq 4, one can construct a curve like that in Figure 3 that predicts the activation barriers for a group of like reactions, i.e. those with the same AEo*. Experimental values for 16 such transfer reactions were found to be well modeled by the Marcus equation curves. The authors stated that while the results were consistent with a Marcus theory interpretation, more data were needed. These data were to appear in subsequent years, largely in terms of proton and especially methyl group transfer. The breakdown of the linear Bronsted relation was predicted some 60 years ago in the original paper? but the technical expertise needed to observe such curvature had developed sufficiently only by the early 1960's, when Eigen and co-workers uncovered such behavior in fast proton transfer in solution.24 Slower protontransfer reactions-such as between carbon bases capable of charge delocalization-had been known to exhibit linearity over a pK range as large as 10 units. In contrast to this, Eigen's work has produced a number of curved Bronsted plots over ranges of only a few pK units. Expression 5 provides an explanation as to why one would expect a Bronsted plot to be more curved for a faster proton transfer. Differentiating eq 5 with respect to A E O , gives (6),which describes
-d-a - - 1 dAEo
(6)
8AEo*
the variation of a as a function of AEo*, the intrinsic barrier. As fast eq 6 indicates, reactions with smaller AEo*'s-i.e. reactions-would be predicted to show more Bronsted curvature. Thus, for a given AEo range, a varies more quickly for smaller AEo* values. For example, for AEo* = 1 kcal/mol, (Y changes from 0 to 1 over a range of 5 pK units in catalyst strength, while for AEo* = 10 kcal/mol this transition range expands to 55 pK units.25 In the latter case, a typical experimental range of 5-10 pK units is insufficient to engender a large change in a, and hence the linear Bronsted plots. As an example of the role of the intrinsic barrier in gas-phase proton-transfer reactions, the rates of proton transfer in systems that are able to delocalize the negative charge have been examined." The slow rates observed are evidence of large intrinsic barriers, analogous to the solution-phase results. These studies have since been extended to include proton transfer between substituted benzyl anions, in which the slow rates again imply fairly large barriers.26 An aspect of the Marcus analysis that lends itself to experimental verification is the additivity postulate,16which dictates that the intrinsic barrier to some cross reaction AX B A XB should be the mean of the barriers to the corresponding self-reactions AX + A A + XA and BX + B B XB. For
-
+
-
(24) Eigen, M. Angew. Chem., Inl. Ed. Engl. 1964, 3, 1. (25) Kresge, A. J. Chem. SOC.Rev. 1973, 2, 475. (26) Han, C.-C., unpublished results.
-
+
+
TABLE I: SN2Reactions with Observed Efficiencies below Detection Limits" in Accord with Prediction AH' ,'
reaction methodb kcalimol Exchange Reactions D- + CH4 + H- + CHpD FA^ -0 CDpO- + CHpOCHp + CHp0- + CDpOCHp ICR' -0 CD3S- + CHpSCH3-N+ CHpS- + CDpSCHp ICRf -0 Cross Reactions t-BuO- + CH3F + F + r-BuOCH, HCC- + CHpF ++ F + HCCCHp CN- + CHpF + F + CH3CN OH- + CHpOCHp ++ CHpO- + CHpOH NHC + CH30CH3-x, CH30- + CH3NH2
ICR~
FAg FA8
FA^
FAh
-
-7 -24 -5
-6 -19
"Detection limits: Eff 10-4(FA), -10-3(ICR). bFA = flowing afterglow, ICR = ion cyclotron resonance. 'Calculated from data in ref 49a,b. dReference49c. 'Reference 4b. 'Reference 5 . ZReference 41. * Bierbaum, V. M., personal communication. instance, given the "experimental" intrinsic barriersS for the SN2 reaction C1- CH3Cl (10 kcal/mol) and for CH30- + CH3CI (27 kcal/mol), one would predict a barrier of 44 kcal/mol for CH30- CH30CH3,and the reaction should be immeasurably slow. Indeed the reaction is experimentally too slow to measure in the gas phase.5 (The slowness of the same reaction in solution is usually attributed to C H 3 0 - being a "poor leaving group", or to unfavorable solvation effects, rather than to the importance of a large intrinsic barrier.) Other gas-phase SN2 reactions, both self and cross, that have low efficiencies in accord with Marcus theory are shown in Table I. Wolfe, Mitchell, and Schlegel provided a more quantitative test of the Marcus equation when they performed ab initio calculations on gas-phase SN2 reactions.*' Their results indicate that the transition-state structure parameters, such as bond lengths and angles, can be correlated with the exothermicity, but the energies cannot, implying that some nonthermodynamic factor is intervening. The authors identified this factor as the Marcus intrinsic barrier. Proceeding further, they discovered a nearly perfect correlation between the cross reaction activation energies predicted from the Marcus equation and from ab initio calculation. Predictions can also be made concerning primary kinetic isotope effects in gas-phase ion-molecule reactions. In the absence of tunneling, isotope effects arise from differences in zero-point energies and sums of states. For a linear proton transfer between two "heavy" groups A and B, the maximum effect should occur in the case of a symmetric transition state, or more precisely, one in which the masses and bond strengths are such that the hydrogen does not move in the symmetric stretching ~ i b r a t i o n ~(eq * ~ *7). ~
+
+
AH
+B
-
[A-H-B]*
-
A
+ HB
(7)
Thus, a thermoneutral reaction exhibits a maximum kinetic isotope effect, and the isotope effect decreases as the reaction becomes progressively more exothermic (Le. the transition state becomes more asymmetric).2s Because this prediction could be experimentally tested in a straightforward manner, it motivated numerous studies of proton-transfer rates in solution.29 These studies generally support the model described above. Data from gas-phase ion-molecule reactions are less plentiful, although much of the rate data seems to be in accord with the behavior outlined In addition, results that seem at (27) Wolfe, S.;Mitchell, D. J.; Schlegel, H.B. J . Am. Chem. SOC.1981, 103, 7692, 7694. (28) Westheimer, F. H. Chem. Rev. 1961, 61, 265. (29) More OFerrall, R. A. In "Proton Transfer Reactions", Caldin, E., Gold, V., Eds.; Wiley: New York, 1975; Chapter 8. (30) Noest, A. J.; Nibbering, N. M. M. Inl. J . Mass Specrrom. Ion Phys. 1980, 34, 383. (31) Jasinski, J. M.; Brauman, J. I. J . Am. Chem. SOC.1980, 102, 2906. (32) Tumas, W.; Foster, R. F.; Brauman, J. I. J . Am. Chem. SOC.1984, 106, 4053. (33) Tumas, W.; Foster, R. F.; Pellerite, M. J.; Brauman, J. I. J . Am. Chem. SOC.1983, 105, 7464.
The Journal of Physical Chemistry, Vol. 90, No. 3, 1986 475
Structure and Reactivity in Ionic Reactions SCHEME I 0-
‘CH1
I
CH;
’CH,
SCHEME Il
Products
N
f
2
odds with the isotope effect/exothermicity relationship can be explained in terms of perturbation of the reaction profile that may result, for instance, in a change in the rate-determining step.28 For example, Neest and Nibbering examined the deprotonation reaction of acetone-I , l , l - d 3by various alkoxide bases using ion cyclotron resonance s p e ~ t r o m e t r y .The ~ ~ relative rates of proton and deuterium abstraction depend on the strength of the base; the weakest base, t-BuO-, exhibits the largest kinetic isotope effect, in accord with prediction. In addition, kinetic isotope effects for proton transfer between substituted pyridine bases in the gas phase were observed to decrease as the exothermicity of the reaction increased.31 In this study, the relatively small isotope effects (1.1-1.8) were consistent with the transition-state energies and vibrational frequencies chosen to reproduce the experimental efficiencies. The relationship between isotope effects and exothermicity can also be observed in proton-transfer reactions within a complex produced by infrared multiple photon absorption32 (Scheme I). The mechanism shown has been inferred for tertbutoxide ion by deuterium labeling on the methyl groups and examination of product acetone enolate isotope ratios.,, The cleavage produces the intermediate at an energy near the barrier to proton transfer. Substitution of different R groups (Me, Ph, CF,) renders the proton-transfer step progressively less exothermic, resulting in enhanced deuterium isotope effects (kH/kD = 1.6,2.5, 6.0 r e ~ p e c t i v e l y ) . ~ ~ Another study concerned with deuterium isotope effects points out that the intrinsic barrier to proton transfer may vary with the particular anion used. Bierbaum et al., in their study of the base induced elimination of diethyl ethers (C4HI0Oand C4D100 by NH2- and OH-), observe a larger kinetic isotope effect for the more exothermic r e a ~ t i o n , which )~ utilizes amide ion as the base. Thus, while the amide reaction is more exothermic than the hydroxide reaction, the barrier for proton transfer to amide is larger, suggesting a larger intrinsic barrier. Noest and Nibbering comment30 that the isotope effect in the deprotonation of acetone by NH2- does not fit the trend exhibited by alkoxide ions. Finally, Wellman et al. have reported kinetic isotope effects in the deprotonation of substituted toluenes by alkoxide bases.35 While reasonable isotope effects were observed for the exothermic reactions, inverse effects (kH/kD < 1) were observed for the reactions within a few kcal/mol of thermoneutrality. Inverse isotope effects are typically observed in preequilibrium proton transfers, suggesting that in this case the rate-determining step follows the proton transfer (Scheme 11). For exothermic reactions, the rate constants defining the equilibrium Kq do not compete with the dissociation to products, and the isotope effects are determined by the relative frequencies of H and D abstraction. (34) Bierbaum, V. M.; Filley, J.; D e h y , C. H.; Jarrold, M. F.; Bowers, M. T . J . Am. Chem. Soc. 1985, 107, 2818. (35) Wellman, K. M. Victoriano, M. E.; Isolani, P. C.; Riveros, J. M. J . Am. Chem. Soc. 1919, 101, 2242. (36) Klass, G.;Underwood, D. J.; Bowie, J. H. A m . J. Chem. 1981, 34, 507.
For thermoneutral reactions, however, the equilibrium Kq becomes competitive with dissociation and indeed apparently controls product partitioning. Complex 2 is calculated to be somewhat more stable than complex 1. V. Empirical Correlations Nucleophilic substitution and proton-transfer reactions are two of the most important and extensively studied chemical processes. Nucleophiles and (Lewis) bases are isoelectronic species and both enter into a chemical reaction by donating a pair of unshared electrons. Based on many reactions studied in solution, it has been established empirically that strong bases are also usually good nucleophile^.^^ While there are exceptions and limitations, this simple empirical rule has been widely accepted. On the other hand, gas-phase studies employing Marcus theory, which allows the separation of a measured reaction energy barrier into kinetic and thermodynamic contributions, have established that the intrinsic kinetic barrier actually increases with the basicity of the n~cleophile,~ Le., the “intrinsic nucleophilicity” decreases with increasing basicity. The experimentally observed activation barrier is the result of a mixing of thermodynamic driving force into the intrinsic kinetic barrier as it is manifest in Marcus theory. It is well-known that reaction exothermicity has the effect of decreasing the effective reaction barrier; this effect is embodied in the Bronsted equation. Since basicity is reflected in thermodynamic instability, the more basic a nucleophile, the more exothermic is its substitution reaction, and the faster the reaction rate. Consequently, the observed empirical relationship that nucleophilicity usually parallels basicity is mostly due to the increased thermodynamic driving force associated with a strong base. Basicity is a thermodynamic property that is directly related to the heterolytic X-H bond dissociation energy. Nucleophilic reactivity, however, is a kinetic property which also contains a thermodynamic component. It depends on both the substrate and the nucleophile. Additionally, there can be steric and other interactions (e.g. ~ y m b i o s i s ) ? ~Therefore, ,~~ a correlation between basicity and nucleophilicity cannot be guaranteed. Reactions in solution are always affected by the solvation of reactants; the reversal in the acidity order of simple alcohols in solution as compared to the gas phase is a well-known example of this.39 Thus it is desirable to establish a set of correlations for intrinsic molecular properties in the absence of solvation phenomena. Systematic studies on gas-phase ion-molecule methyl transfer and SN2 reactions have been carried out in our laboratory4,40as well as in other^.^^^^ These processes have also been examined t h e ~ r e t i c a l l y . ~ ~ ~ ~ ~ In attempts to find a correlation from which nucleophilicity in methyl transfer reactions could be predicted, SN2 intrinsic barriers have been plotted against such nucleophile properties as the gas-phase proton affinity, PA (defined in eq 8), electron HX
-
H+ + X-
PA(X-) = AHoga= Do(H-X) - EA(X)
+ IP(H)
(8b)
(37) For a brief review of nucleophilicity vs. basicity in solution see. Lowry,
T. H.; Richardson, K. S. “Mechanism and Theory in Organic Chemistry“, 2nd ed; Harper & Row: New York, 1981; Chapter 4. Streitwieser, A., Jr.; Heathcock, C. H. “Introductionto Organic Chemistry”, 2nd ed.; Macmillan: New York, 1981; pp 164-169. (38) Brauman, J. I.; Olmstead, W. N.; Lieder, C. A. J . Am. Chem. SOC. 1974, 96, 4030. (39) (a) Brauman, J. I.; Blair, L. K. J . Am. Chem. SOC.1968, 90,5636, 6561. Ibid. 1969, 91, 2126. Ibid. 1970, 92, 5986. (b) For examples in solution, see ref 37. (40) Dodd, J. A.; Brauman, J. I. J . Am. Cliem. SOC.1984, 106, 5356. (41) Tanaka, K.; Mackay, G. I.; Bohme, D. K. Can. J . Chem. 1976, 54, 1643. (42) (a) Chandrasekhar, J.; Smith, S. F.; Jorgensen, W. L. J . Am. Chem. SOC.1984,106,3049. (b) Chandrasekhar, J.; Smith, S. F.; Jorgensen, W. L. J . Am. Chem. SOC.1985,107, 154. (c) Morokuma, K. J. J . Am. Chem. Soc. 1982, 104, 3732. (d) Raghavachari, K.; Chandrasekhar, J.; Burnier, R. C. J . Am. Chem. SOC.1984, 106, 3124. (e) Roos, B. 0.;Kraemer, W. P.; Diercksen, G . H. F. Theor. Chim. Acta (Berlin) 1976, 42, 77. (0 Carrion, F.; Dewar, M. J. S. J . Am. Chem. SOC.1984, 106, 3531.
476 The Journal of Physical Chemistry, Vol. 90, No. 3, 1986
120
:
Han et al.
HCiC
cl
40-
AE;
-
1
I
320
I
I
1
380
1
360
340
,
hcal/mole
AH~(HX-. H'+ XI
i-
I
OL';O
I
I
1
im
100
I
140
Figure 5. Relation between nucleophilicity, represented by the intrinsic reaction barrier, and basicity, expressed as the gas-phase proton affinity of the nucleophile.
I
kcaf/mole
D"(H-x) Figure 4. Relation between Do(CH3-X) and Do(H-X). The slope of the least-squares line is 0.70, see text.
x-
RY
[ X-R-Y]-*
RX
+
Y-
detachment energy, and homolytic bond dissociation energy; nevertheless, the best correlation was obtained when the intrinsic barrier was plotted against the gas-phase methyl cation affinity (MCA) of the nucleophile5 (eq 9). It should be noted43that the CH3X MCA(X-) =
AH09a
-
CH3+
+ X-
= DO(CH3-X) - EA(X)
(9a)
+ IP(CH3) (9b)
correlation is equally good for A,??,,*plotted against MCA plus a constant, for instance the quantity Do - EA. MP9,is the energy change associated with reaction 9a, and Do, EA, and IP are the homolytic bond dissociation energy, electron affinity, and ionization potential of the respective species labeled in the parentheses. It was found that as the methyl cation affinity of the nucleophile X- increases, so does the height of the intrinsic barrier for the exchange reaction X-CH3X XCH3.X- (Le. the nucleophilicity decreases). We can write a similar equation for the gas-phase proton affinity, PA (eq 8). For most common nucleophiles Do(CH3-X) correlates linearly with Do(H-X), as shown in Figure 4. Because of the contribution from the EA(X) term, one generally cannot get a good correlation between the PA(X-) and MCA(X-) (in other words, basicity and nucleophilic exothermicity) unless the slope for a Do(CH3-X) vs. Do(H-X) plot is unity. Given that the MCA is a good measure of intrinsic nucleophilicity5 and that the slope for a Do(CH3-X) vs. Do(H-X) plot is not unity, a good correlation between intrinsic nucleophilicity and basicity (PA) is not e x p e ~ t e d .On ~ the other hand, the slope in the homolytic bond dissociation energy plot is not far from unity; thus, a rough trend of decreasing intrinsic nucleophilicity with increasing basicity can still be seen. Not unexpectedly, the points scatter more widely in an intrinsic nucleophilicity-basicity plot, Figure 5, than in an intrinsic nucleophilicity-MCA plot.5 In Figure 4 it is apparent that two of the nucleophiles, H C C and CN, do not fall on the least-squares line. The linear fit of all but the sp and sp2 hybridized nucleophiles is remarkably good. H C C and C N (reacting at carbon) are special in that they are sp hybridized; for instance, this accounts for the difference between their bond dissociation energies and those with sp3 hybridization. For sp2-hybridized species, e.g. phenyl, vinyl, and acetyl, this "off-line" character is also apparent, although less so. Within each hybridization group there is a linear correlation between homolytic bond dissociation energies to methyl and hydrogen. Therefore, we did not include these five nucleophiles in determining the slope of the least-squares fit of the data in Figure 4. Although H C C and CN are not perfectly fit in an intrinsic nucleophilicity-MCA
protic solvent
-
~~
~
(43) We are grateful to Professor S. S. Shaik for discussion of this matter.
R i A C T I O N COORDINATE
Figure 6. Potential energy surfaces for S N reactions ~ in different media.
plot,5 the correlation is worse when considering intrinsic nucleophilicity vs. PA; the MCA represents the more successful property in predicting nucleophilicity. VI. Solution vs. Gas Phase For typical SN2reactions the absolute reaction rates increase 4-5 powers of ten upon changing from protic to dipolar aprotic solvents, and increase by another 10 powers of 10 when the reaction is carried out in the gas phase.4b The origin of this dramatic change in reactivity, and also the irregular reactivity (vide infra) of some nucleophiles, is mainly attributable to specific solvation of the reactants. As shown in Figure 1, a typical gas-phase ion-molecule reaction does not require activation energy. When a gas-phase reaction is moved into a polar aprotic solvent all of the species-the reactants, transition state, and products-are stabilized by solvation. Therefore, the whole reaction potential surface in solution is lower than that in the gas phase, as illustrated in Figure 6. The isolated nucleophile has concentrated charge distribution and is strongly solvated and stabilized; the ionmolecule complexes and the transition state, on the other hand, have relatively dispersed charge distribution and are not as strongly solvated. This differential solvation results in the single energy barrier characteristic of most reactions in solution. The transition from a double minimum potential surface appropriate for gasphase SN2reactions to one with a single barrier has been reproduced in a recent theoretical s t ~ d y . ~ "The , ~ barrier increases when protic solvents are used due to strong hydrogen bonding to the negatively charged nucleophile. When the nucleophile has high
J. Phys. Chem. 1986, 90, 477-481 charge density, e.g. F, enhanced differential solvation effects will further increase the barrier. Since the differential solvation of the reactants and the transition state is highly dependent on the reaction medium, it is not surprising to see anomalous reactivity patterns when reactions in different media are compared. In protic solvents, for instance, the order of reactivity of the halide ions toward a given substrate is I- > Br- > C1- > F,while in both polar aprotic solvents and in the gas phase the order is reversed. Also, in a recent of the nucleophilic reactivity as a function of the standard oxidation potential of the nucleophile, thiolates were found to deviate from the linear correlation obtained for first row elements. This effect, thought to arise from polarizability differences, might also come about through solvation phenomena; thiolates fit well on the intrinsic nucleophilicity-MCA correlation line in the gas phase.5 Although there are difficulties in interpreting ionic reactions in solution, these studies have provided an incredible amount of knowledge about structure-reactivity relationships. Along this line, Marcus theory has played an important role as discussed in section 111. The structure of the transition state has always been an intriguing subject. For an sN2 reaction, one would like to know the transition-state charge distribution, and also whether it is tight or loose, reactantlike or productlike. From available information on methyl transfer reactions in protic solvents, Albery and Kreevoy21carrived at the conclusion that the total bond order between the methyl center and the nucleophile and the leaving group is less than 1, Le., looser than a structure conforming to bond order conservation. Also, when substituents are placed on the transferring methyl group for sN2 reactions in aprotic solvents, positive Hammett p values often result.21c The authors concluded that the transition state is tighter than that for the same reaction in protic solvents, in which negative p's are observed. They attributed this difference to variations in solvation ability. While this explanation is consistent with available data, it is not unique. Alternatively, the transition state has similar structure in different solvents. The net negative charge in the transition state is sufficiently dispersed in the protic solvent that substituents (44) Ritchie, C. D. J . Am. Chem. Soc. 1983, 105, 7313.
477
located on the methyl group seem to be responding to a partial positive charge (relative to reactant). Such effective charge dispersion is not provided in an aprotic solvent, and the substituent on the methyl center is required to help disperse the net negative charge, resulting in an apparent positive p . This interpretation is supported by preliminary results from our labor at^#^ on gas-phase C1- exchange reactions at substituted benzyl centers, (eq lo), which yield a p value of +0.6. Given the
+
37C1- ArCH2SCI
-
+
37C1CH2Ar 35Cl-
(10)
full negative charge in the (unsolvated gas phase) transition state, one would have expected a larger positive value of p . This experiment bears on the A&* vs. MCA plot discussed above, in that the rather small&value of p supports our suggestion5that a positive charge partially develops at the methyl center in sN2 reactions. The correlation of A&* with MCA implies both net breaking of the CH3-X bond and net negative charge on X in the sN2 transition state. Since the reactants incorporate a full negative charge on X, it seems likely that X collectively bears more than unit charge, and that CH3is positively charged as a consequence. The observed substituent effect in reaction 10 appears to reflect a modest positive charge at the methyl center coupled with the overall negative charge of the system.
Acknowledgment. We are grateful to the National Science Foundation for support of this research and for Fellowship support to J.A.D., who currently holds the F. R. Veatch Fellowship. (45) Dodd, J. A.; Brauman, J. I., unpublished results. (46) Other gas-phase studies of substituent effects in anionic systems usually show large positive values of p. For instance, both the acidities of substituted aceto henones4' and the electron affinities of substituted acetophenone enolates$s have yielded p values of about +8 (47) Bartmess, J. E.; Scott, J. A.; McIver, R. T., Jr. J . Am. Chem. SOC. 1979, 101, 6056. (48) Jackson, R. L.;Zimmerman, A. H.; Brauman, J. I. J . Chem. Phys. 1979, 71, 2088. The paper incorrectly reports a p of twice this value. (49) (a) Benson, S. W. "Thermochemical Kinetics", 2nd ed.; Wiley-Interscience: New York, 1976. (b) Bartmess, J. E.; McIver, R. T., Jr. In "Gas Phase Ion Chemistry", Bowers, M. T., Ed.; Academic Press: New York, 1979; Vol. 1. (c) Payzant, J. D.; Tanaka, K.; Betowski, L. D.; Bohme, D. K. J . Am. Chem. SOC.t976, 98, 894.
Internal Energy Effects in Ion-Molecule Reactions: NH,'"
+ D,
Paul R. Kemper and Michael T. Bowers* Department of Chemistry, University of California, Santa Barbara, California 93106 (Received: July 22, 1985)
The reaction of NH3+ with D2 is reported as a function of NH3+vibrational energy and NH3+/D2center-of-mass kinetic energy. Vibrational energy in NH3+is varied from 1 to 5 eV by using selective charge-transfer reactions to form the NH3+ ion. Calibration procedures for specifying the amount of internal energy in NH3+ for a specific charge-transfer reagent have previously been reported in the literature. Kinetic energy is varied by established ICR double resonance techniques over the range 0-1 eV (CM). All experiments are performed on the UCSB tandem ICR. Two reaction channels are observed: NH3D+ D (D atom abstraction) and NH2D++ HD (H/D exchange). Both reactions are extremely inefficient at thermal energies even though the first channel is exoergic by 1.07 eV and the second is thermal neutral. The results indicate that vibrational energy in NH3+strongly and exclusively drives the H/D exchange channel and kinetic energy strongly and exclusively drives the D atom abstraction channel. The results are compared with those of other workers and possible mechanisms discussed.
+
-
Introduction The reactions of NH3+ and H2/D2 (1) originally attracted NH3+ + H2 NH4+ + H + 1.07 eV (1) interest due to its being both exothermic and inefficient. Kim and Huntress' found the rate coefficient to be ( 3 f 1) X
cm3/s (using D2). The corresponding reaction efficiency is kexp/kmlhion 2.5 X lo4. This very low efficiency was apparently explained when Fehsenfeld et aL2 measured the temperature and kinetic energy dependence of reaction 1. Their data indicated that a barrier to reaction of approximately 0.09 eV was present. They argued that such a barrier probably occurred early on the
(1) J. K. Kim, L. P. Theard, and W. T. Huntress, Jr., J. Chem. Phys., 62, 45 (1975).
(2) F. C. Fehsenfeld, W. Lindinger, A. L.Schmeltekopf, D. L. Albritton, and E. E. Ferguson, J . Chem. Phys., 62, 2001 (1975).
+
0022-3654/86/2090-0477$01.50/0
0 1986 American Chemical Society
