observation of transition-state vibrational thresholds in the rate...

4
that was inclined by 150 from the horizontal plane is shown in Fig. 3. The speeds of the drops varied across the gradient and with the size of the drop; average speeds of 1 to 2 min/s were observed for 1- to 2-pl1 drops on the steeper part of the gradient (17). The shape of the drop shown in Fig. 3 is that of a spherical cap. The difference of the con- tact angles in the advancing and receding edges of the drop was only -2° to 3°. The effect of gravity on the drop shape was not significant here because the radius of the drop (1 to 1.5 mm) was smaller than the Laplace length (2.7 mm) (18). The near- spherical shape of the drop appears to be a consequence of the equilibration of the La- place pressure inside the drop, which is consistent with the model proposed by Bro- chard (3). Water was not the only liquid that moved across such gradient surfaces; other liquids such as glycerol and chloroform also moved. The motion of these liquids was, however, examined with a horizontal gra- dient surface. Although we have not studied these fac- tors in any detail, the speeds of the liquid drops depended on the hysteresis in contact angles, the surface tension and viscosity of the drops, the drop volume, the steepness of the gradient, and the inclination of the gradient surface. Detailed understanding of the kinetics of drop motion on gradient surfaces should take these factors into ac- count. The gradient surfaces reported here are easily prepared. They should be useful in the study of the motion of liquid drops induced by chemical gradients and of the interplay of chemical and thermal gradients. REFERENCES AND NOTES 1. H. Bouasse, Capillarit6 et Ph6nombnes Superfi- cielles (Delagrave, Paris, 1924). 2. N. 0. Young, J. S. Goldstein, M. J. Block, J. Fluid Mech. 6, 350 (1959). 3. F. Brochard, Langmuir 5, 432 (1989). 4. K. D. Barton and R. S. Subramanian, J. Colloid Interface Sci. 133, 211 (1989). 5. A. W. Adamson, Physical Chemistry of Surfaces (Wiley, New York, ed. 3, 1976). 6. R. L. Cottington, C. M. Murphy, C. R. Singleterry, Adv. Chem. Ser. 43, 341 (1964). 7. E. Raphael, C. R. Acad. Sci. Paris Ser. 11306, 751 (1988). 8. T. Ondarcuhu and M. Veyssie, J. Phys. (Paris) 111, 75 (1991). 9. H. Elwing, S. Welin, A. Askendal, U. Nilsson, I. Lundstrom, J. Colloid Interface Sci. 119, 203 (1987). 10. C.-G. Golander, Y.-S. Un, V. Hlady, J. D. Andrade, Colloids Surf. 49, 289 (1990). 11. These values of speed are approximate and vari- able. The effects of drop volumes on speeds have not been rigorously examined. Qualitatively, it was observed that the speeds increased as the vol- ume of the drops increased. 12. Silicon wafers were cleaned in hot piranha solution, which is a mixture of 70% H2SO4 and 30% H202 (30% solution in water). The wafer was placed in this solution for 30 min. Afterward, the wafer was thoroughly rinsed with and stored in distilled water. Before we prepared the gradient surface, the wafer was rinsed again in running distilled water and then dried by blowing nitrogen over it. 13. We found that immersing the wafer in warm dis- tilled water and rinsing it in pure distilled water helped to remove some of the loosely adsorbed contamination from the surface. The gradient sur- face can be easily contaminated by atmospheric impurities. The surface remained clean, however, when kept immersed in pure distilled water. 14. Drops used to measure the advancing and reced- ing contact angles were held stationary on the surface of the silicon wafer by the tip of the microsyringe used to form the drops. The contact angles were measured under quasistatic condi- tions, that is, after the cessation of the movement of the contact line. For quantitative correlation between drop velocity and surface energy gradi- ent, the contact angles should be measured un- der dynamic conditions. These measurements are beyond the scope of this study. 15. The thickness gradients of the monolayers were functions of the adsorption times and molecular weights of the silanes. We have also prepared gradient surfaces with Cl3Si(CH2)7CH3. After a 5-min adsorption, a close-packed, nearly com- plete monolayer (11 A thick) was formed at the hydrophobic edge. 16. The thickness obtained by ellipsometry was an average over an area of -3 mm2. 17. The length (5 mm) of this gradient corresponds to what was detected by ellipsometry, which also matched the field of view of the telescope used to observe the motion of water drops. When the drop moved beyond 5 mm from the hydrophobic edge, the drop became flat and thin in the region of weaker gradient. 18. The Laplace length (also known as the capillary length) is (yL/jpg)0 5, where p is the density of the liquid and g is the acceleration due to gravity. 19. M.K.C. acknowledges support from Dow Corning Corporation. G.M.W. acknowledges support from the Office of Naval Research and the Defense Advanced Research Projects Agency. We thank M. J. Owen (Dow Coming) for many valuable discussions. 9 January 1992; accepted 15 April 1992 Observation of Transition-State Vibrational Thresholds in the Rate of Dissociation of Ketene Edward R. Lovejoy, Sang Kyu Kim, C. Bradley Moore Rate constants for the dissociation of highly vibrationally excited ketene (CH2C0) have been measured at the threshold for the production of CH2(3B1) and CO(11+). The rate constant increases in a stepwise manner with increasing energy, consistent with the long-standing premise that the rate of a unimolecular reaction is controlled by flux through quantized transition-state thresholds. The data give the energies of the torsional and C-C(0 bending vibrations of the transition state. The elementary chemical reaction is one of the most fundamental processes in na- ture, and the theoretical and experimental study of the transformation of reactants into products has been an important area of research for many decades. Experimental studies of unimolecular reactions of highly energized molecules provide strong tests of the theories developed to describe chemical reactivity (1). The unimolecular rate theo- ry of Rice, Ramsperger, Kassel, and Marcus (RRKM) (2) is based on the assumptions that (i) the vibrational energy in the excit- ed molecule is distributed statistically among all the vibrational degrees of free- dom, (ii) the energy flows freely among the different degrees of freedom at a rate much faster than the reaction rate, and (iii) the rate of reaction is controlled by the passage through a transition state located at the dynamical bottleneck separating the reac- tant from products on the potential energy surface for the reaction. In the region of the transition state, the bound vibrational mo- tions of the molecule are not coupled to the reaction coordinate, and passage through Chemical Sciences Division of the Lawrence Berkeley Laboratory and Department of Chemistry, University of California, Berkeley, CA 94720. SCIENCE * VOL. 256 * 12 JUNE 1992 the transition state is vibrationally adiabat- ic. In this sense, the vibrational levels of the transition state represent reaction thresholds, that is, quantized channels con- necting the reactant to products. The energy dependence of the RRKM rate constant for a molecule with a fixed energy (E) and total angular momentum (J) is given by k(E,J) = WI(EJ)/[hp(EJ)] (3) where W*(EJ) is the number of vibrational levels of the transition state with energy less than E, p(EJ) is the density of vibrational states of the reactant (number of states per unit energy), and h is Planck's constant. Definitive tests of RRKM theory are hampered by the difficulty in evaluating the individual terms in Eq. 1. Historically, the density of reactant states Ip(EJ)I has been estimated by extrapolating a normal mode treatment of the molecular vibrations to higher energies (3). However, recent spec- troscopic studies show that the actual den- sity of states for a number of molecules is significantly higher (five to ten times for 10,000 cm- t < E < 30,000 cm-') (4) than predicted by the normal mode picture. The number of accessible reaction channels at 1541 --- 111 gnnungnnunRRRMRRcmmnmRngmm -. -- on June 22, 2007 www.sciencemag.org Downloaded from

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Page 1: Observation of Transition-State Vibrational Thresholds in the Rate …cdnl.kaist.ac.kr/LABjournal/science1.pdf · 2016-02-24 · ordinate. This well is meant to represent the eight

that was inclined by 150 from the horizontalplane is shown in Fig. 3. The speeds of thedrops varied across the gradient and with thesize of the drop; average speeds of 1 to 2min/s were observed for 1- to 2-pl1 drops onthe steeper part of the gradient (17). Theshape of the drop shown in Fig. 3 is that ofa spherical cap. The difference of the con-tact angles in the advancing and recedingedges of the drop was only -2° to 3°. Theeffect of gravity on the drop shape was notsignificant here because the radius of thedrop (1 to 1.5 mm) was smaller than theLaplace length (2.7 mm) (18). The near-spherical shape of the drop appears to be aconsequence of the equilibration of the La-place pressure inside the drop, which isconsistent with the model proposed by Bro-chard (3).

Water was not the only liquid thatmoved across such gradient surfaces; otherliquids such as glycerol and chloroform alsomoved. The motion of these liquids was,however, examined with a horizontal gra-dient surface.

Although we have not studied these fac-tors in any detail, the speeds of the liquiddrops depended on the hysteresis in contactangles, the surface tension and viscosity ofthe drops, the drop volume, the steepness ofthe gradient, and the inclination of thegradient surface. Detailed understanding ofthe kinetics of drop motion on gradientsurfaces should take these factors into ac-count. The gradient surfaces reported hereare easily prepared. They should be useful inthe study of the motion of liquid dropsinduced by chemical gradients and of theinterplay of chemical and thermal gradients.

REFERENCES AND NOTES

1. H. Bouasse, Capillarit6 et Ph6nombnes Superfi-cielles (Delagrave, Paris, 1924).

2. N. 0. Young, J. S. Goldstein, M. J. Block, J. FluidMech. 6, 350 (1959).

3. F. Brochard, Langmuir 5, 432 (1989).4. K. D. Barton and R. S. Subramanian, J. Colloid

Interface Sci. 133, 211 (1989).5. A. W. Adamson, Physical Chemistry of Surfaces

(Wiley, New York, ed. 3, 1976).6. R. L. Cottington, C. M. Murphy, C. R. Singleterry,

Adv. Chem. Ser. 43, 341 (1964).7. E. Raphael, C. R. Acad. Sci. Paris Ser. 11306, 751

(1988).8. T. Ondarcuhu and M. Veyssie, J. Phys. (Paris) 111,

75 (1991).9. H. Elwing, S. Welin, A. Askendal, U. Nilsson, I.

Lundstrom, J. Colloid Interface Sci. 119, 203(1987).

10. C.-G. Golander, Y.-S. Un, V. Hlady, J. D. Andrade,Colloids Surf. 49, 289 (1990).

11. These values of speed are approximate and vari-able. The effects of drop volumes on speeds havenot been rigorously examined. Qualitatively, it wasobserved that the speeds increased as the vol-ume of the drops increased.

12. Silicon wafers were cleaned in hot piranha solution,which is a mixture of 70% H2SO4 and 30% H202(30% solution in water). The wafer was placed inthis solution for 30 min. Afterward, the wafer wasthoroughly rinsed with and stored in distilled water.Beforewe prepared the gradient surface, the waferwas rinsed again in running distilled water and

then dried by blowing nitrogen over it.13. We found that immersing the wafer in warm dis-

tilled water and rinsing it in pure distilled waterhelped to remove some of the loosely adsorbedcontamination from the surface. The gradient sur-face can be easily contaminated by atmosphericimpurities. The surface remained clean, however,when kept immersed in pure distilled water.

14. Drops used to measure the advancing and reced-ing contact angles were held stationary on thesurface of the silicon wafer by the tip of themicrosyringe used to form the drops. The contactangles were measured under quasistatic condi-tions, that is, after the cessation of the movementof the contact line. For quantitative correlationbetween drop velocity and surface energy gradi-ent, the contact angles should be measured un-der dynamic conditions. These measurementsare beyond the scope of this study.

15. The thickness gradients of the monolayers werefunctions of the adsorption times and molecularweights of the silanes. We have also preparedgradient surfaces with Cl3Si(CH2)7CH3. After a

5-min adsorption, a close-packed, nearly com-plete monolayer (11 A thick) was formed at thehydrophobic edge.

16. The thickness obtained by ellipsometry was anaverage over an area of -3 mm2.

17. The length (5 mm) of this gradient corresponds towhat was detected by ellipsometry, which alsomatched the field of view of the telescope used toobserve the motion of water drops. When the dropmoved beyond 5 mm from the hydrophobic edge,the drop became flat and thin in the region ofweaker gradient.

18. The Laplace length (also known as the capillarylength) is (yL/jpg)0 5, where p is the density of theliquid and g is the acceleration due to gravity.

19. M.K.C. acknowledges support from Dow CorningCorporation. G.M.W. acknowledges support fromthe Office of Naval Research and the DefenseAdvanced Research Projects Agency. We thankM. J. Owen (Dow Coming) for many valuablediscussions.

9 January 1992; accepted 15 April 1992

Observation of Transition-State VibrationalThresholds in the Rate of Dissociation of Ketene

Edward R. Lovejoy, Sang Kyu Kim, C. Bradley MooreRate constants for the dissociation of highly vibrationally excited ketene (CH2C0) havebeen measured at the threshold for the production of CH2(3B1) and CO(11+). The rateconstant increases in a stepwise manner with increasing energy, consistent with thelong-standing premise that the rate of a unimolecular reaction is controlled by flux throughquantized transition-state thresholds. The data give the energies of the torsional andC-C(0 bending vibrations of the transition state.

The elementary chemical reaction is oneof the most fundamental processes in na-ture, and the theoretical and experimentalstudy of the transformation of reactants intoproducts has been an important area ofresearch for many decades. Experimentalstudies of unimolecular reactions of highlyenergized molecules provide strong tests ofthe theories developed to describe chemicalreactivity (1). The unimolecular rate theo-ry of Rice, Ramsperger, Kassel, and Marcus(RRKM) (2) is based on the assumptionsthat (i) the vibrational energy in the excit-ed molecule is distributed statisticallyamong all the vibrational degrees of free-dom, (ii) the energy flows freely among thedifferent degrees of freedom at a rate muchfaster than the reaction rate, and (iii) therate of reaction is controlled by the passagethrough a transition state located at thedynamical bottleneck separating the reac-tant from products on the potential energysurface for the reaction. In the region of thetransition state, the bound vibrational mo-tions of the molecule are not coupled to thereaction coordinate, and passage throughChemical Sciences Division of the Lawrence BerkeleyLaboratory and Department of Chemistry, University ofCalifornia, Berkeley, CA 94720.

SCIENCE * VOL. 256 * 12 JUNE 1992

the transition state is vibrationally adiabat-ic. In this sense, the vibrational levels ofthe transition state represent reactionthresholds, that is, quantized channels con-necting the reactant to products.

The energy dependence of the RRKMrate constant for a molecule with a fixedenergy (E) and total angular momentum (J)is given by

k(E,J) = WI(EJ)/[hp(EJ)] (3)where W*(EJ) is the number of vibrationallevels of the transition state with energy lessthan E, p(EJ) is the density of vibrationalstates of the reactant (number of states perunit energy), and h is Planck's constant.

Definitive tests of RRKM theory arehampered by the difficulty in evaluating theindividual terms in Eq. 1. Historically, thedensity of reactant states Ip(EJ)I has beenestimated by extrapolating a normal modetreatment of the molecular vibrations tohigher energies (3). However, recent spec-troscopic studies show that the actual den-sity of states for a number of molecules issignificantly higher (five to ten times for10,000 cm-t < E < 30,000 cm-') (4) thanpredicted by the normal mode picture. Thenumber of accessible reaction channels at

1541

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the transition state [Wt(EJ)] is even moredifficult to evaluate because of the lack ofknowledge of the properties of the short-lived transition state. Generally, the vibra-tional frequencies of the transition state areestimated by extrapolating from the proper-ties of the stable molecule. However, high-level quantum mechanical calculations nowprovide quantitative predictions for theproperties of transition states of small mole-cules (5).RRKM theory predicts that the rate

constant increases by steps with an ampli-tude equal to 1/[hp(EJ)J as the energy ofthe reactant is increased through each vi-brational state of the transition state. In thepast, experiments have lacked the energyresolution and control of the angular mo-mentum needed to resolve possible transi-tion-state structure in the energy depen-dence of a rate constant. In this work, rateconstants for the unimolecular dissociationof ketene were measured with an energyresolution much finer than the expectedvibrational energy spacing at the transitionstate. The energy dependence of the rateconstant exhibits clear steplike structures.Analysis of these structures provides astrong test of the basic tenets of unimolec-ular reaction rate theory.

The lowest energy dissociation channelfor ketene yields triplet methylene [CH2CO-- CH2(3B1) + CO('1+)l (Fig. 1) with athreshold 28,250 cm-' above the zero pointenergy of ground-state ketene. There is asmall barrier along the reaction coordinate

E

-

>h5SDcwU

C0c-.-

H.HC=C=0

Reaction coordinateFig. 1. A schematic representation of the dis-sociation of triplet ketene. The reaction coordi-nate corresponds to the distance between thecarbon atoms. The solid lines represent thepotential energy for the ground singlet (So), thefirst excited singlet (S1), and the first triplet (T.)electronic states. The transition state, whichseparates the highly vibrationally excited reac-tant from the products, is depicted as a singlepotential well perpendicular to the reaction co-ordinate. This well is meant to represent theeight bound vibrations of the transition state.

(about 1300 cm` above the energy of theseparated fragments), which controls thedynamics of the energy release to the sepa-rating fragments (6, 7). This barrier defines adistinct bottleneck to the reaction, and thetriplet ketene decomposition represents amodel case for testing RRKM theory.

Highly vibrationally excited ketene wasprepared by tunable pulsed laser excitation ofketene cooled in a supersonic jet expansion.Strong electronic-vibrational coupling in theenergized molecule yields an excited state thatis a statistical (8) mixture of the groundsinglet (So), excited singlet (S1), and triplet(T1) states. The jet cooling (rotational tem-perature 5 K) and narrow bandwidth of theultraviolet excitation laser (0.4 cm-1) mini-mized the uncertainty in the energy and an-gular momentum of the excited molecules.We measured rate constants for the uni-

molecular decomposition of ketene bymonitoring the appearance of the CO (vibra-tional level v = 0,J4 = 12) fragment as afunction of time after ketene excitation. TheCO photofragnent was detected by vacuumultraviolet laser-induced fluorescence (LIE).The experimental conditions and datatreatment are as described (6, 7). Rateconstants were measured at energy incre-ments of 2 to 4 cm-1, and the measure-ments were repeated over the entire ener-gy range three times. The average disso-ciation rate constant (Fig. 2, curve a)exhibits clear steps in the first few hundredwave numbers above an initial step asso-ciated with the zero point vibrational levelof the transition state.

Photofragment excitation (PHOFEX)spectra of the CO product were also taken.The LIF signal from specific CO(vJP) rovi-

Fig. 2. CH2CO dissociation 30rate constant and PHOFEXdata. Curve a, experimen-tal rate constants for theunimolecular decay ofketene. Curve b, CO(v =

0,Jp = 12) PHOFEX signal.Curve c, PHOFEX spec-trum calculated from the iiexperimental rate constant 10data. Curve d, CO(v=0=p= 2) PHOFEX signal. Theactual ratio of the yields ofCO(v = 0,JP = 12) to CO(v= 0,Jp = 2) is about 20:1 0at 28,500 cm-1 for CH2CO(7).

brational states was measured at a fixedreaction time (At) as a function of theketene excitation energy (E). The PHO-FEX signal can be expressed as

S(E,vjp,At) Xc

a(E) P(E,vJp) (1 - e-k(E) At) (4)where cr(E) is the ketene absorption crosssection, P(E,v,J) is the yield or branchingratio for the (v,Jp) quantum state of CO,and k(E) is the ketene dissociation rateconstant. The absorption cross section isunstructured at the energies accessed in thisstudy and does not contribute significantlyto the structure in the PHOFEX spectra.For small reactive conversion Ik(E) At < <1], the PHOFEX signal is proportional tothe rate constant and the CO(vJ0) yield.

The PHOFEX spectrum of CO v = 0p= 12) at 50 ns (Fig. 2, curve b) shows clearsteps that match those in the rate constant.A plot of (1 - e-k(E) At) based on theexperimental k(E) data and a reaction timeof 50 ns is shown in Fig. 2, curve c. Thereis a strong correspondence between thissimulated PHOFEX spectrum and the ex-perimental spectrum for E < 28,500 cm-1,indicating that the PHOFEX structure forthe CO(v = 0,Jp = 12) state is dominatedby the variation of the rate constant withexcitation energy. The abrupt change in slopeof the CO(v = 0j, = 12) PHOFEX spectrumat 28,500 cm-' reflects a sudden decrease inthe fractional yield of JP = 12. The rateconstant continues to rise sharply in thisregion. The PHOFEX spectrum of theCO(v = 0 1 = 2) product (Fig. 2, curve d)is significantliy different, suggesting that theenergy dependence of the CO(v = 0,Jp =

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28,200 28,400 28,600Eneg (a')

SCIENCE * VOL. 256 * 12 JUNE 19921542

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2) yield contributes to the structure in thePHOFEX spectrum of the low-J product.

The CD2CO decomposition rate con-stant (Fig. 3, curve a) increases in a distinctstepwise pattern with increasing energy, butwith smaller energy spacing between thesteps as compared to that observed forCH2CO. The narrower spacing is consis-tent with the expected decrease in thevibrational frequencies of the transitionstate upon isotopic substitution. The PHO-FEX spectrum for the CO(v = 0,Jp = 12)product from CD2CO at 200 ns, and aspectrum calculated from the k(E) data areshown in Fig. 3, curves b and c, respective-ly. As is the case for CH2CO, the CO(v =0j = 12) and simulated spectra are verysimilar, suggesting that the structure in theCO(v = 0,Jp = 12) PHOFEX spectrum isattributable predominantly to the structurein the CD2CO rate constant. A PHOFEXspectrum of the CO(v = 0,Jp = 2) productfrom the dissociation of CD2CO at a delaytime of 150 ns is shown in Fig. 3, curve d.Similar to the results for CH2CO, addition-al sharp features are observed in the low-JPPHOFEX spectrum for CD2CO, indicatingthat the energy dependence of the low JPCO yield is structured.

Allen and Schaefer have performed so-phisticated quantum mechanical calcula-tions for the dissociation of triplet ketene(9). The calculations describe a transitionstate that has a strongly bent C-COOframework [about 1160 versus 180° (linear)for the ground statel and a C-C bond thatis extended by about 40% relative to theground state. The lowest frequency vibra-tions at the transition state are the torsionbetween the CH2 and CO portions of the

Fig. 3. CD2CO data (see 12legend to Fig. 2). I

molecule, the C-C-O bend (252 cm-'),and the CH2 wag (366 cm- 1). The torsion-al motion is a hindered internal rotationwith an ab initio barrier of 380 cm` . Theab initio CH2CO hindered rotor potentialgives a spacing of about 140 cm1 betweenthe first two states, which is larger than thespacing between the first two steps in thedata. The calculated hindered rotor spacingfor CD2CO is about 20% lower than forCH2CO, which is in good agreement withthe fractional difference in the energy spac-ings of the first two steps in the data forCH2CO and CD2CO.A significant fraction (0.22) of the po-

tential energy released as the CH2 and COfragments repel each other appears as rota-tional energy of the CO fragment, consis-tent with the strongly bent C-C-O geom-etry of the transition state and rapid releaseof the energy along the C-C bond (7).The angular momentum imparted to theCO is reproduced very well by a simpleclassical model that assumes that theavailable energy is released impulsivelyalong the C-C bond at the transitionstate. This model predicts only the frac-tion of energy released to rotation (that is,only one JP value for CO) and not thedistribution of angular momentum. Theshapes of the CO rotational distributionsare derived from the vibrational motion ofthe molecule when the C-C bond breaks(7). This dynamical model predicts thateach vibrational state of the transitionstate, with its characteristic motion, givesa unique distribution of angular momen-tum in the products. The variation in theCO(v J) yield with energy is reflected inthe P-OFEX spectra. Therefore, these

I ailI,,, ,,, I.,,. aaA, 100

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M ~ ~ ~ 0

28,250 28,450 28,650End (a)

SCIENCE * VOL. 256 * 12 JUNE 1992

spectra contain detailed information aboutthe vibrational character of the transition-state thresholds.

For example, the CO(v = 0,J1p = 2)PHOFEX spectrum exhibits two sharp fea-tures at about 28,500 and 28,600 cm-1which are absent from the CO(v = 0,Jp =12) spectrum but which correlate with thesudden change in slope in the CO(v =0,Jp = 12) spectrum. The prominence ofthese features in the low JP spectrumindicates that the transition state thresh-olds at these energies involve atomic mo-tions that enhance the production of COin low JP states. The spacing betweenthese features is comparable to the spacingbetween the first two pronounced steps inthe PHOFEX spectra, suggesting that thestates are combinations of the lowest en-ergy hindered rotor states with an excitedstate of a different vibrational mode. Theexcited (v = 1) C-C-O bend is a likelyassignment for these thresholds becausethe bending motion adds or subtracts sig-nificant angular momentum from the im-pulsive release and broadens the CO JPdistribution. The broadening increases theyield of low JP products and decreases theyield ofJP states near the maximum of thedistribution (IPi 12). This assignmentgives a C-COO bending energy of 250 + 10cm-1 at the transition state, which agreesvery well with the ab initio value of 252cm-1 (9).

The dissociation rate for deuteratedketene is significantly slower than for thehydrogen isotopomer, because the deuterat-ed compound has a larger density of reac-tant states [p(Ej)J owing to its reducedvibrational frequencies. The rate constantmeasured at the top of the second promi-nent step for CH2CO (28,360 cm-') is 4.0+ 0.8 times the CD2CO rate constant atthe same position (28,410 cm-'), suggest-ing that the CD2CO density of states is fourtimes the CH2CO state density at theseenergies. The ratio of harmonic state den-sities (3) is 3.6:1. The absolute density ofreactant states is difficult to evaluate be-cause of uncertainties in the number oftransition-state levels that contribute toeach step in the rate constant (10).

The observation of steps in the rateconstant supports the concept that the rateof a unimolecular reaction with a well-defined barrier (and hence transition state)is controlled by flux through quantized tran-sition-state thresholds. Results for the dis-sociation of singlet ketene (11) show that itremains much more difficult to define thetransition state and the dynamics of energyflow for reactions without barriers. Thecomparison of experimental and ab initiodata given here also demonstrates thatmany properties of the transition state arepredicted by theory.

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REFERENCES AND NOTES

1. For reviews, see: F. F. Crim, Annu. Rev. Phys.Chem. 35, 657 (1984); H. Reisler and C. Wittig,ibid. 37, 307 (1986).

2. R. A. Marcus and 0. K. Rice, J. Phys. ColloidChem. 55, 894 (1951); R. A. Marcus, J. Chem.Phys. 20, 359 (1952); W. Forst, Theory of Unimo-lecular Reactions (Academic Press, New York,1973).

3. G. Z. Whitten and B. S. Rabinovitch, J. Chem.Phys. 38, 2466 (1963).

4. E. Abramson, R. W. Field, D. Imre, K. K. Innes, J.L. Kinsey, ibid. 83, 453 (1985); W. F. Polik, D. R.Guyer, C. B. Moore, ibid. 92, 3453 (1990); A.Geers, J. Kappert, F. Temps, W. Wiebrecht, Ber.Bunsenges. Phys. Chem. 94, 1219 (1990); Y. S.Choi and C. B. Moore, J. Chem. Phys. 94, 5414(1991).

5. C. E. Dykstra, Annu. Rev. Phys. Chem. 32, 25(1981); C. W. Bauschlicher, S. R. Langhoff, P. R.Taylor, Adv. Chem. Phys. 77, 103 (1990).

6. I.-C. Chen and C. B. Moore, J. Phys. Chem. 94,263 (1990).

7. _ , ibid., p. 269.8. The character of the excited state is mostly that of

highly vibrationally excited ground singlet be-cause of the overwhelming density of groundsinglet states at these energies. The harmonicdensities of vibrational states are 1.2 x 104 (SO),15 (S,), and 60 (T1) per cm~1 at 28,250 cm-'above the SO zero point level.

9. W. D. Allen and H. F. Schaefer Ill, J. Chem. Phys.89, 329 (1988).

10. An upper limit for the density of CH2CO states canbe calculated by assuming that the first two rateconstant steps represent two hindered rotor lev-els, which are each triply degenerate as a result ofthe electron spin. If this is the case, the density ofCH2CO states is 4.5 x 104 per cm-' at 28,360cm-', which is about four times the harmoniccount.

11. S. J. Klippenstein and R. A. Marcus, J. Chem.Phys. 93, 2418 (1990); W. H. Green, Jr., A. J.Mahoney, 0.-K. Zheng, C. B. Moore, ibid. 94,1961 (1991).

12. Supported by the Director, Office of Energy Re-search, Office of Basic Energy Sciences, Chemi-cal Sciences Division of the U.S. Department ofEnergy under contract DE-AC03-76SF00098.

6 February 1992; accepted 21 April 1992

However, a carbene complex has neverbeen observed in a catalytic system (3). Analternative mechanism that has been dis-cussed is nucleophilic attack of the diazocompound on a metal-alkene or complex(Eq. 2) (4).

L-T/LL

ETR

CrtL

- - L-t- INi/ILL

00ReWN2AR, L

~~~Lsyn + aWilmiure (2)

Mechanism of the Rhodium Porphyrin-CatalyzedCyclopropanation of Alkenes

Jana L. Maxwell, Kathlynn C. Brown, David W. Bartley,Thomas Kodadek*

The rhodium porphyrin-catalyzed cyclopropanation of alkenes by ethyl diazoacetate (EDA) isrepresentative of a number of metal-mediated cydopropanalion reactions used widely inorganic synthesis. The active intermediate in these reactions is thought to be a metal carbenecomplex, but evidence for the involvement of metalolefin ir complexes has also been pre-sented. Low-temperature infrared and nudear magnetic resonance spectroscopies have beenused to characterize a rhodium porphyrin-diazoalkyl adductthat results from the stoichiometriccondensation of the catalyst and EDA. Optical spectrscopy suggests that this complex is thedominant steady-state species in the catalytic reaction. This compound decomposes thermallyto provide cyclopropanes in the presence of styrene, suggesting that the carbene is indeed theactive intermediate. Metal-alkene iTr complexes have also been detected spectroscopically.Kinetic studies suggest that they mediate the rate of carbene formation from the diazoalkylcomplex but are not attacked directly by EDA.

The design of asymmetric catalysts for use insynthesis has emerged as one of the mostimportant problems in modem organic chem-istry because most biologically active com-pounds are chiral. Recently, there has been agreat deal of interest in the development ofmetal-based asymmetric cyclopropanationcatalysts (1) for the synthesis of pyrethroidinsecticides, d-tum peptide mimics, and anumber of other interesting compounds. Wehave concentrated on rhodium porphyrin cat-alysts and have developed moderately enanti-oselective systems for the cyclopropanation ofalkenes by diazo esters. In order to rationallydesign more effective asymmetric pockets, it isimportant to understand in detail the mech-anism of the reaction, including the nature ofthe reactive intermediates and the arrange-ment of atoms in the transition state. Thiswill allow a rational positioning of groups inthe chiral cavity to more effectively influence

1544

the approach of the prochiral substrate to themetal. Unfortunately, despite considerableinvestigation, many aspects of the mechanismof metal-catalyzed cyclopropanations remainunclear. Current speculation is that the cata-lyst reacts with the diazo compound to pro-duce an electrophilic metal carbene that issubsequently attacked by the alkene to pro-vide the cyclopropane and regenerate thecatalyst (Eq. 1) (2).

V LL ALLZ L. 2 L

WA.R* + L,kLsyn +ant Lmixture

Re

(1)

Nucleophilic additions to metal-alkenecomplexes are common in organometallicchemistry (5), and r complexes have beencharacterized for some cyclopropanationcatalysts (4). However, the precise role ofthese species is unclear. Other mechanismsare also possible. We report a mechanisticanalysis of the rhodium porphyrin-cata-lyzed cyclopropanation of alkenes by ethyldiazoacetate (EDA) (6) that clarifies thesematters. Our results, including the charac-terization of a reactive organometallic in-termediate, provide strong evidence for theintermediacy of a metallocarbene and alsoreveal a novel role for the substrate as anaxial ligand that moderates the rate ofcarbene formation when the catalyst has alabile ligand such as iodide.

In order to probe for the possible forma-tion of a reactive rhodium porphyrin car-bene, we investigated the stoichiometricreaction of EDA with a rhodium porphyrinin the absence of alkene. Addition of aslight excess of EDA to a CD2CI2 solutionof iodorhodium tetra(p-tolyl) porphyrin(RhTTPI) at -400C results in a rapid,subtle color change and formation of aporphyrin-EDA adduct. The 'H nuclearmagnetic resonance (NMR) spectrum ofthis species exhibits a single set of resonanc-es attributable to the protons of the EDA-derived fragment (Fig. 1). Each signal isshifted upfield relative to its position inEDA, demonstrating that these protons sitabove the face of the aromatic macrocycle,which has a strong diamagnetic ring cur-rent. The proton a to the carbonyl carbonis a doublet, although a two-dimensionalcorrelated (2-D COSY) spectrum showsthat it is not coupled to any other proton.Therefore, the splitting is due to coupling

Department of Chemistry and Biochemistry, Universityof Texas at Austin, Austin, TX 78712.

*To whom correspondence should be addressed.

SCIENCE * VOL. 256 * 12 JUNE 1992

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