Reactive Intermediate Chemistry

922 REACTIONS ON THE FEMTOSECOND TIME SCALE

A similar understanding has emerged from recent semiclassical trajectory calculations for organic reactions: Each molecule gives a product defined by the potential energy surface, the specific distribution of vibrational energy among the available modes, and the relative phases among these modes. The reaction outcome is not dependent on the potential energy surface alone. The overall distribution of products and energies observed represents the composite of all of the individual vibrational-mode-and-phase distinctive reactant molecules as each follows its trajectory.

In a variety of ways, deuterium-substituted reactants can provide vital information on dynamics: Substantial isotope effects point to vibrational modes playing a key role in dynamics, and vice versa.

The once rather ephemeral transition state construct derived from logic and statistical mechanics, a virtual entity, has emerged as an experimental reality. Structural changes associated with specific nuclear vibrations in energized molecules in the transition region may be correlated with reaction dynamics.

The transition state concept, once understood in static terms only, as the saddle point separating reactants and products, may be fruitfully expanded to encompass the transition region, a landscape in several significant dimensions, one providing space for a family of trajectories and for a significant ‘‘transition state lifetime.’’ The line between a traditional transition structure and a reactive intermediate thus is blurred: The latter has an experimentally definable lifetime comparable to or longer than some of its vibrational periods.

SUGGESTED READING

D. L. Smith, ‘‘Coherent Thinking,’’ Eng. Sci. 1999, LXII (4), 6.

O. M. Sarkisov and S. Ya. Umanskii, ‘‘Femtochemistry,’’ Russ. Chem. Rev. 2001, 70, 449.

M. Chergui, ‘‘Femtochemistry,’’Chimia 2000, 54, 83.

G.Roberts, ‘‘Femtosecond Chemical Reactions,’’ Philos. Trans. R. Soc. London A 2000, 358, 345.

R.Hoffmann, ‘‘Pulse, Pump & Probe,’’ Am. Sci. 1999, 87, 308. See also R. Hoffmann, Am. Sci. 1998, 86, 326; 1999, 87, 21; 2000, 88, 14.

A.H. Zewail, ‘‘Femtochemistry,’’ J. Phys. Chem. 1993, 97, 12427.

A.H. Zewail, ‘‘Transient Species at Femtosecond Resolution,’’ Proc. Robert A. Welch Found. Conf. Chem. Res. 1994, 38, 129.

A.H. Zewail, ‘‘Femtochemistry: Recent Progress in Studies of Dynamics and Control of Reactions and Their Transition States,’’ J. Phys. Chem. 1996, 100, 12701.

A.H. Zewail, ‘‘Femtochemistry: Chemical Reaction Dynamics and Their Control,’’ Adv. Chem. Phys. 1997, 101, 3, 892.

A.H. Zewail, ‘‘Femtochemistry. Atomic-scale Resolution of Physical, Chemical and Biological Dynamics,’’ Proc. Robert A. Welch Foundation Conf. Chem. Res. 1997, 41, 323.

A.H. Zewail, ‘‘Femtochemistry: Atomic-Scale Dynamics of the Chemical Bond Using Ultrafast Lasers (Nobel lecture),’’ Angew. Chem., Int. Ed. Engl. 2000, 39, 2586.

REFERENCES 923

A.H. Zewail, ‘‘Femtochemistry: Atomic-Scale Dynamics of the Chemical Bond,’’ J. Phys. Chem. A 2000, 104, 5660.

A.H. Zewail, ‘‘Femtochemistry. Past, Present, and Future,’’ Pure Appl. Chem. 2000, 72, 2219.

REFERENCES

The references cited here depend heavily on investigations reported by the Professor Ahmed H. Zewail, the 1999 Nobel Laureate in Chemistry, and his collaborators at the California Institute of Technology. In them, one will find extensive citations of work leading up to recent advances in femtochemistry as well as to contemporary studies from other laboratories.

1.Y. Jean, L. Salem, J. S. Wright, J. A. Horsley, C. Moser, and R. M. Stevens, Pure Appl. Chem., Suppl. (23rd Congr., Boston) 1971, 1, 197.

2.J. A. Horsley, Y. Jean, C. Moser, L. Salem, R. M. Stevens, and J. S. Wright, J. Am. Chem. Soc. 1972, 94, 279.

3.S. J. Baskin and A. H. Zewail, J. Chem. Educ. 2001, 78, 737.

4.J. C. Polanyi and A. H. Zewail, Acc. Chem. Res. 1995, 28, 119.

5.A. H. Zewail and R. B. Bernstein, Chem. Eng. News 1988, Nov. 7, 24.

6.R. Hoffmann, Am. Sci. 1999, 87, 308.

7.A. H. Zewail, Laser Phys. 1995, 5, 417.

8.A. H. Zewail, Angew. Chem., Int. Ed. Engl. 2001, 40, 4371.

9.A. H. Zewail, Nature (London) 2001, 412, 279.

10.M. J. Rosker, T. S. Rose, and A. H. Zewail, Chem. Phys. Lett. 1988, 146, 175.

11.T. S. Rose, M. J. Rosker, and A. H. Zewail, J. Chem. Phys. 1988, 88, 6672.

12.V. Engel, H. Metiu, R. Almeida, R. A. Marcus, and A. H. Zewail, Chem. Phys. Lett. 1988,

152, 1.

13.A. H. Zewail, J. Phys. Chem. A 2000, 104, 5660.

14.H. Guo and A. H. Zewail, Can. J. Chem. 1994, 72, 947.

15.M. H. M. Janssen, M. Dantus, H. Guo, and A. H. Zewail, Chem. Phys. Lett. 1993, 214, 281.

16.C. Ko¨tting, E. W. G. Diau, J. E. Baldwin, and A. H. Zewail, J. Phys. Chem. A 2001, 105, 1677.

17.C. Ko¨tting, E. W. G. Diau, T. I. Sølling, and A. H. Zewail, J. Phys. Chem. A 2002, 106, 7530.

18.E. W. D. Diau, J. Casanova, J. D. Roberts, and A. H. Zewail, Proc. Nat. Acad. Sci. U. S. A. 2000, 97, 1376.

19.S. De Feyter, E. W. G. Diau, and A. H. Zewail, Phys. Chem. Chem. Phys. 2000, 2, 877.

20.S. K. Kim, S. Pedersen, and A. H. Zewail, J. Chem. Phys. 1995, 103, 477.

21.S. K. Kim and A. H. Zewail, Chem. Phys. Lett. 1996, 250, 279.

22.S. K. Kim, J. Guo, J. S. Baskin, and A. H. Zewail, J. Phys. Chem. 1996, 100, 9202.

23.E. W. G. Diau, C. Ko¨tting, T. I. Sølling, and A. H. Zewail, ChemPhysChem 2002, 3, 57.

924REACTIONS ON THE FEMTOSECOND TIME SCALE

24.T. I. Sølling, E. W. G. Diau, C. Ko¨tting, S. De Feyter, and A. H. Zewail, ChemPhysChem 2002, 3, 79.

25.E. W. G. Diau, C. Ko¨tting, and A. H. Zewail, ChemPhysChem 2001, 2, 273.

26.E. W. G. Diau, J. Herek, Z. H. Kim, and A. H. Zewail, Science 1998, 279, 847.

27.S. Pedersen, J. L. Herek, and A. H. Zewail, Science 1994, 266, 1359.

28.E. W. G. Diau, C. Ko¨tting, and A. H. Zewail, ChemPhysChem 2001, 2, 294.

29.J. Bigeleisen and M. G. Mayer, J. Chem. Phys. 1947, 15, 261.

30.J. Bigeleisen, J. Chem. Phys. 1949, 17, 675.

31.J. E. Baldwin, in The Chemistry of the Cyclopropyl Group, Vol. 2, Z. Rappoport, Ed., John Wiley & Sons, Inc., Chichester, 1995, pp. 469–494.

32.R. Baum, Chem. Eng. News 1994, Nov. 28, 6.

33.J. E. Baldwin, T. B. Freedman, Y. Yamaguchi, and H. F. Schaefer, J. Am. Chem. Soc. 1996, 118, 10934.

34.C. Doubleday, Jr., J. Phys. Chem. 1996, 100, 3520.

35.C. Doubleday, Jr., K. Bolton, G. H. Peslherbe, and W. L. Hase, J. Am. Chem. Soc. 1996, 118, 9922.

36.C. Doubleday, Jr., Chem. Phys. Lett. 1995, 233, 509.

37.C. Doubleday, Jr., K. Bolton, and W. L. Hase, J. Phys. Chem. A 1998, 102, 3648.

38.C. Doubleday, Jr., K. Bolton, and W. L. Hase, J. Am. Chem. Soc. 1997, 119, 5251.

39.K. Bolton, W. L. Hase, and C. Doubleday, Jr., Ber. Bunsen-Ges. Phys. Chem. 1997, 101, 414.

40.E. M. Goldfield, Faraday Discuss. 1998, 110, 185.

41.S. De Feyter, E. W. G. Diau, A. A. Scala, and A. H. Zewail, Chem. Phys. Lett. 1999, 303, 249.

42.A. A. Scala, E. W. D. Diau, Z. H. Kim, and A. H. Zewail. J. Chem. Phys. 1998, 108, 7933.

43.E. W. G. Diau, S. De Feyter, and A. H. Zewail, Chem. Phys. Lett. 1999, 304, 134.

44.B. A. Horn, J. L. Herek, and A. H. Zewail, J. Am. Chem. Soc. 1996, 118, 8755.

45.D. K. Lewis, B. Brandt, L. Crockford, D. A. Glenar, G. Rauscher, J. Rodriquez, and J. E. Baldwin, J. Am. Chem. Soc. 1993, 115, 11728.

46.D. K. Lewis, D. A. Glenar, S. Hughes, B. L. Kalra, J. Schlier, R. Shukla, and J. E. Baldwin, J. Am. Chem. Soc. 2001, 123, 996.

47.S. Wilsey, K. N. Houk, and A. H. Zewail, J. Am. Chem. Soc. 1999, 121, 5772.

48.H. Ihee, V. A. Lobastov, U. M. Gomez, B. M. Goodson, R. Srinivasan, C.-Y. Ruan, and A. H. Zewail, Science 2001, 291, 458.

49.J. Cao, H. Ihee, and A. H. Zewail, Chem. Phys. Lett. 1998, 290, 1.

50.H. Ihee, J. S. Feenstra, J. Cao, and A. H. Zewail, Chem. Phys. Lett. 2002, 353, 325.

51.S. Zilberg, and Y. Haas, J. Am. Chem. Soc. 2002, 124, 10683.

52.H. Ihee, J. Kua, W. A. Goddard, III, and A. H. Zewail, J. Phys. Chem. A 2001, 105, 3623.

53.H. Ihee, A. H. Zewail, and W. A. Goddard, III, J. Phys. Chem. A 1999, 103, 6638.

54.H. Ihee, B. M. Goodson, R. Srinivasan, V. A. Lobastov, and A. H. Zewail, J. Phys. Chem. A 2002, 106, 4087.

55.Y. Tanimura, K. Yamashita, and P. A. Anfinrud, Proc. Natl. Acad. Sci. U. S. A. 1999, 96, 8823.

recognizes that there might be a continuum of possibilities from a synchronous concerted process, in which all of the bonding changes occur to the same extent at the same time, through varying degrees of asynchronous transformation, to the final limit of a stepwise process in which, say, one bond is fully broken before a second one begins to break. In order to try to formulate a better defined mechanistic inquiry, one might therefore recast the question to ask whether the reaction involves an intermediate. At first sight, it would seem that the stepwise mechanistic limit would require the creation of an intermediate, but, as we will see, even this attempted clarification cannot always produce a black-or-white, experimentally testable question.

The issue is conveniently illustrated with examples from nominally pericyclic reactions, where the controversy about concertedness has been the most heated. The first example is the vinylcyclopropane rearrangement,2 depicted (somewhat unrealistically as we will see) in Scheme 21.1. The overall transformation is clear: One must break the bond between C1 and C2 of the reactant, and then reconnect C2 to C30. The controversy resides in the details of the stereochemistry and timing of these two events.3 First the stereochemistry: The bond formation at C2 can occur with retention or inversion of its original configuration. In addition, the bond formation at C30 can occur to the same face (suprafacial) of the allylic unit (C1 C20 C30) to which C2 was originally attached, or to the opposite face (antarafacial). These two stereochemical variables combine to create four possible stereoisomeric products, for which the two-letter designations are shown in Scheme 21.1. Experimental study of the stereochemistry would appear to allow one to differentiate between two extremes of the timing question. If the breaking of the C1 C2

Scheme 21.1. The four possible stereoisomeric cyclopentenes-d2 that could be formed by C1 C2 scission of the indicated single enantiomer of vinylcyclopropane-d2. One possible mechanism, involving interconverting achiral biradicals, is also depicted. The pairs of letters under each product isomer indicate the stereochemical changes between reactant and product. Note that in an actual experiment, the reaction would be complicated by competitive C1 C3 scission. In this scheme s ¼ superfacial, a ¼ antarafacial, r ¼ retention, and i ¼ inversion.

928 POTENTIAL ENERGY SURFACES AND REACTION DYNAMICS

bond and the formation of the C2 C30 bond occurred concertedly, the reaction would be pericyclic (a [1,3] sigmatropic rearrangement) and, hence, subject to the Woodward–Hoffmann rules of orbital symmetry conservation.4 These rules indicate that, for a thermal reaction, the products designated si and ar would be ‘‘allowed’’ whereas the other pair, sr and ai, would be ‘‘forbidden.’’ The alternative, stepwise mechanism would presumably involve the singlet-state biradical depicted in Scheme 21.1. On average, this biradical might be expected to be achiral (in the same way that butane is achiral despite the fact that some of its low-energy conformations are chiral). In addition, it might be expected to undergo facile internal rotations about the remaining C C bond to C2. Since the intermediate is achiral, and since achiral intermediates are supposed to give only achiral or racemic products, this mechanism would seem to predict that the product isomers related to each other as enantiomers should be formed in equal amounts, namely, [sr] ¼ [ai] and [si] ¼ [ar].

Before discussing the experimental results, let us make the connection to the topic of this section—PE profiles. The representation of concerted or stepwise mechanisms on a PE profile seems clear cut. If the reaction is stepwise it involves an intermediate, appearing as a local minimum on the PE profile—such as that near the center of the profile in Figure 21.1. On the other hand, a concerted reaction can have no intermediate, and so its PE profile should have just a reactant minimum and a product minimum connected by a single transition state.

In reality, the reaction could not be persuaded to go exactly as shown in Scheme 21.1, because the C1 C3 bond would certainly break at very nearly the same rate as C1 C2. In the experiments actually conducted by Baldwin et al.,3c this problem was resolved by deuterium labeling both C2 and C3—creating diastereomerically pure, but achiral molecules. Even then, there remained a large number of technical difficulties, which in the end the researchers were able to overcome. Their results indicated that the four stereochemical courses for the reaction run at 300 C were sr 23%, si 40%, ar 13%, and ai 24%. These numbers do not fit the expectations from either mechanism. Clearly, the Woodward–Hoffmann ‘‘forbidden’’ and ‘‘allowed’’ products are formed in nearly equal amounts ([sr] þ [ai] ¼ 47%; [si] þ [ar] ¼ 53%)—hardly what one would expect for a pericyclic reaction. On the other hand, the stereochemical paths do not show the pairwise equalities expected from the stepwise mechanism.

The current explanation of these results comes from a combination of high-level ab initio electronic-structure calculations and molecular-dynamics simulations (see Section 3).5 The picture that emerges from the electronic-structure calculations is that breaking the C1 C2 bond of the reactant creates a biradical that sits on a kind of plateau on the PES. This means that the biradical can undergo a variety of quite substantial geometrical changes that are accompanied by very little (<1 kcal/mol) change in its PE. There are exits to all four possible products from the plateau region, with little or no barrier to the formation of any of them. This situation cannot be depicted in a traditional PE profile because of its overly compressed dimensionality. Furthermore, the kinetics of such reactions cannot be properly described by the traditional statistical models, such as Rice–Ramsperger–Kassel–Marcus

(RRKM) or transition state theory (TST) (see Section 2). The product ratios are determined by the detailed dynamics of the reaction, as described in Section 3.

There is computational and/or experimental evidence that a structurally diverse range of singlet biradicals occupy plateau-like regions of their PESs.6 A selection of them, including the reactions that they mediate, are shown in Scheme 21.2. The occurrence of a plateau at a mechanistically crucial region of the PE hypersurface guarantees that there can be no clear distinction between ‘‘concerted’’ and ‘‘stepwise’’ mechanisms, and also strongly indicates that the reaction may be one whose course will not be describable by any simple kinetic model.

A plateau on the PE hypersurface is not the only feature that can serve to muddy the distinction between concerted and stepwise reactions. Another occurs when an intermediate, even one in a quite deep PE ‘‘well,’’ is located off the direct path from reactant to product. An example comes from the nominal [3,3] sigmatropic rearrangement of 1,2,6-heptatriene. If heated alone, in the gas phase, the reactant rearranges cleanly to the [3,3] product, 3-methylene-1,5-hexadiene. However, Roth et al.7 showed that an intermediate could be trapped when the reaction was conducted in high-pressure oxygen (!). They postulated that the intermediate was the

Scheme 21.2. Some of the reactions for which there is evidence of mediation by a biradical on an energy plateau. See Ref. (6a–e).

930 POTENTIAL ENERGY SURFACES AND REACTION DYNAMICS

Scheme 21.3. Possible mechanisms for the rearrangement of 1,2,6-heptatriene.

biradical shown in Scheme 21.3. Curiously, when the trapping efficiency was studied as a function of O2 pressure, it was discovered that roughly one-half of the rearrangement occurred without an interceptible intermediate. This observation led the authors to suggest that there must be competitive stepwise and concerted mechanisms for the reaction.7 However, subsequent high-level ab initio calculations by Hrovat et al.8 found no evidence for a pericyclic transition state; only the stepwise pathway could be located. This apparent disagreement between theory and experiment could be rationalized when the detailed geometries of the biradical and the transition states for its formation and conversion to 3-methylene-1,5-hexa- diene were examined. Of particular interest was the dihedral angle between the H8 C1 H9 plane and the C4 C3 H10 plane. In the reactant this dihedral angle is 90 , since the planes in question are at the ends of an allene. Interestingly, in both of the transition states found in the calculations, the corresponding dihedral angle was still near 90 . However, in the biradical intermediate the dihedral angle is 0 in order to achieve allylic stabilization for one of the radical sites. This dihedral-angle difference means that the biradical can be thought of as being displaced from the two transition states along a direction that is roughly at right angles to the reaction coordinate. Figure 21.2 illustrates the point. As a consequence of the PES topology, one can contemplate a mechanism in which some molecules would follow a path (red arrow in Fig. 21.2) from the first transition state directly to and over the second, lower energy one. Other molecules may follow routes (or trajectories, as we will discuss later) that miss the second transition state and, instead fall into the biradical ‘‘trap.’’ The oxygen-trappable intermediate would be generated only by molecules

Figure 21.2. Schematic PE surface for the rearrangement of 1,2,6-heptatriene. The geometrical coordinates, y and R1 R2 are defined as follows: y is the dihedral angle between the H8 C1 H9 and C4 C3 H10 planes. R1 is the C4 C5 distance and R2 is the C2 C7 distance. See Scheme 21.3 for atom numbering (see color insert).

following the general direction of the blue arrow in Figure 21.2.8 Molecular dynamics calculations (see Section 3) have provided support for this picture.9 For the present discussion, the important conclusion is that the mechanistic distinction between stepwise and concerted mechanisms becomes moot on PESs of this kind.

In summary, one can recognize that the familiar PE profile may sometimes hide features of a PE hypersurface that become apparent when even a single additional geometrical coordinate is added to the graph. While the profile may encourage us to think that any reaction involving making or breaking of several covalent bonds should be describable as either stepwise or concerted, the higher dimensional representation reveals that there are probably many reactions for which that distinction is not meaningful.

1.3. Bifurcations and the Nature of Transition States

Most—although, as we will see, not all—of the chemically interesting places on a PES correspond to stationary points—that is, places where the partial first