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		Xl. Cycloaddition reactions
		A. These are reactions of two acyclic molecules to form a cyclic molecule. 1. There are a very large number of these reactions in the organic world. 2. They are extremely useful in a synthetic sense, since two CC bonds are formed. 3. We will not have time to give a comprehensive treat- ment. a. Chapters 10 and 11 in Lowry & Richardson do this. b. You do not have to read all of this material. B. We will concentrate on only one reaction: the dimerization of ethylene to cyclobutane. 1. Energy considerations a. The two CC s bonds formed are stronger than the two CC p bonds broken. i) This is the result despite the ring strain. ii) Using Benson's tables:

		b. DS, however, is negative. i) Two molecules become one. ii) Using Benson's tables: DS₂₉₈ = 44 cal / mol K c. Thus, DG₂₉₈ = 5.9 kcal/mol. i) The reaction is still exothermic and should be ob- servable, however ii) Although DH = 19 kcal/mol, DH for this reaction as shown is incredibly high about 43 kcal/mol. (a) There is no way that it will be observed experimen- tally under normal conditions. (b) One must use very forcing conditions (high tem- peratures, high pressure). 2. Mechanistic questions a.The activation barrier is a function of the reaction mechanism.



	b. For the thermally driven reaction (considered above): i) One clue about the reaction mechanism is that, under some conditions, polymers are formed, i.e. CH₂CH₂(CH₂CH₂ )_n-. ii) Another clue, as we shall see later, is that the reac- tion is completely (or almost completely) stereo nonselective. c. The photochemical reaction is intriguingly different. i) It is quite general, olefins bearing substituents of almost any kind will still produce a cyclobutane. ii) There is virtually no activation energy associated with the reaction if one disregards the amount of energy required to excite the olefin dimer to the excited state. iii) Furthermore, the photochemical reaction not only is stereoselective but it is also stereospecific. C. Before we look at the mechanism for the thermal and photochemical dimerization reaction of olefins, it is useful to first consider another much more simple reaction: H₂+ D₂Æ 2HD 1. This could be considered to be a special sort of cy- cloaddition reaction:

		2. Many experiments have been carried out on this reac- tion. a. Part of the reason for this is that although experimentaly E_a = 41 kcal/mol , an essentially exact M.O. calculation has given E_a = 152 kcal/mol ! b. Yet for the dissociation reaction HH Æ 2H·, DG = only 109 kcal/mol. 3. One possibility that people considered was that this might be a radical chain mechanism, i.e. H-H Æ H· + H· initiation H· + D₂ Æ HD + D· chain propagation D· + H₂ Æ HD + H·



		H· + H· Æ H₂ H· + D· Æ HD chain termination D· + D· Æ D₂ a. Recall that the activation energy comes from mea- suring the rates of reaction. i) If there was a constant, relatively large concentration of H· radicals around or (more probably) if the num- ber of chain propagation steps was very large com- pared to the number of chain termination events then the overall rate would be given by the chain propaga- tion reaction. ii) We saw earlier in the semester that E_a = 11.3 kcal/ mol for H· + H₂ Æ H₂+ H· iii) Alternatively, if the H^. concentration is small or the chain propagation sequence relative to chain termina- tion is small then E_a will approach the bond dissocation energy of H₂ (104 kcal/mol). b. Thus limits for the activation energy expected for a free radical mechanism would be: 11.3 < E_a < 104 kcal/mol; a rather large range! c. Actually since the DG and DG for each step of this reaction is known with some precision, one can calcu- late the concentration of [H^.] and [D^.] that must be present to give the observed reaction rate at a par- ticular temperature. i) This concentration turns out to be pretty large. ii) Researchers have looked long and hard to find any evidence for H^. and D^., but none has been found. iii) Thus the concentration of free radicals (recall this is in the gas phase) is too low to give the experimentally observed rate. 4. Returning to the theoretical calculation why is there a gigantic activation energy associated with this reaction? a. Let us construct a Walsh diagram (an orbital correla- tion diagram) for this reaction. i) There are two mirror planes of symmetry which are always present in the reaction:





	ii) There are several noteworthy points about this diagram. (a) The orbitals for square H₂D₂ are exactly like the p MOs of square cyclobutadiene, and for the same reason that cyclobutadiene distorts to a rectangle, the square H₂D₂ geometry is a high point on the surface. (b) The point of intersection of the AS and SA orbitals is exactly 1/2 of the distance (energetically) between AS and SA at the ground state geometry. (i) However, this point of degeneracy is above the P.E. of H^. + H^. (ii) The energy of stabilization of SA (and SS) is less than the energy by which AS (and AA) is destabilized at the ground state. (c) The HOMO (AS) crosses the LUMO (SA). (i) This is, therefore, a symmetry forbidden reaction. (ii) The two electrons in AS somehow need to jump into the SA orbital. iii) Therefore the amount of energy that



		two electrons in AS need to go up is greater than the energy need to break the HH bond (i.e. the energy difference between AS at the ground state and the P.E. of H^.). Thus, the potential energy surface for the H₂ + D₂ reaction is very replusive. Shown below are two views of the H₂ + H₂ reaction. Each sheet is worth 0.05 atomic units (~30 kcal/mol). These are all potential energies, so a surface with the most negative value is the most stable one. When r₁ = r₂, that plane defines all possible rectangular shapes. The line given by r₁ = r₂ = R defines all possible squares and, finally the geometries for R = 0 are those for all linear ar- rangements of the H₂molecules.

		These calculations are taken from, J. Am. Chem. Soc., 98, 6427 (1976).





		As can be seen there are two tubes of low energy which correspond to the two ways H₂ units can be combined in this coordinate system. Each tube is well- insulated; the potential steeply rises beyond the tube. b. An alternative bimolecular reaction path (the only other one) forms a tetrahedral molecule at the T.S.:



	i) By applying group theory one can easily get the MO's for the H₄ tetrahedron. ii) Again this is a symmetry forbidden reaction with an extremely large activation barrier.




						A triply degenerate set of MOs

			c. An alternative to the dimerization reaction is given by:


			ii)This pathway involves no HOMOLUMO crossing (\ symmetry allowed). iii) There are, however, two problems with this approach. (a) This is a termolecular collision. (i) No known reactions proceed via a real threebody collision. (ii) Furthermore, the DS must be extremely negative and since DG = DH TDS, DH would have to be extremely small. (b) Calculations have given an E_a (DH) for this reac- tion to be 67 kcal/mol. While this is certainly smaller than 151 kcal/mol, it is nonetheless is somewhat too large compared to an experimental barrier of (DG) 43 kcal/mol. iii)The working assumptions by the experimental physical chemists suggesting this (in 1973) were:



	(a) Disregard the theoretical estimate for the three- body collision. (b) Get around entropy effects by postulating the existance of a dimer (a van der Waals dimer?) formed in a preequilibrium step:


	5. The very large difference between theory and experi- ment has been explained only after much effort (1986). a. All of the reactions were carried out in glass (pyrex) tubes. b. It was found that if one carefully treats the inner glass surface then there is no formation of HD from H₂ + D₂! i) This is done by passing (CH₃)₃SiCl through it. ii) The silylilating reagent reacts with OH groups, etc. c. Therefore, the glass surface itself is catalyzing the reaction. i) It causes HH (and DD) bond breakage to form H^. (D^.) radicals close to the surface. ii) These then immediately react with H₂(D₂) by the surface to produce HD ! d. So, there is no disagreement between theory and experiment. e. What is ironic is that organic chemists who do vapor phase pyrrolysis reactions (pyrex tubes) have known for over 20 years before this time that preparation of the glass surface is necessary or else one will get all kinds of extraneous side reactions catalysized by the surface. D. Olefin dimerization the thermal reaction 1. Let us first consider what will happen in a concerted reaction path.




		a. The two CC s bonds are formed at the same rate, i.e. a leastmotion path. b. Again two mirror planes of symmetry are conserved.



			i) In the reactant we are breaking the two bonds, so we need to make the two p and two p* orbitals symmetry correct with respect to m_l and m₂. ii) Likewise, in the product we have formed two CC bonds, thus the two CC s and s* orbitals must be symmetry correct with respect to m_l and m₂. iii) Therefore, linear combinations of the p and p* orbitals are taken:



				The splitting (energy difference) between these com- binations is small since the distance between the two olefins is initially long. iv) Similarly, the CC s and s* orbitals in the product are symmetry correct with respect to m₂ but not m_l, so linear combinations are again taken of them.




	c. An orbital correlation diagram for this concerted process then would be (note: s lower than p, s* higher than p*)



			i) The HOMO and LUMO cross (look carefully at the orbital shapes). ii) Just as with H₂ + D₂ this is symmetry forbidden. iii) There must be a lower activation energy process. 2. The nonconcerted thermal reaction pathway a. The most simple would be to allow one CC bond to form at a faster rate than the other:

			b. For the same reason as the H₂ + D₂ reaction, the crossing point for the concerted reaction occurs at a higher energy than the energy of a p orbital, therefore,

					should lie at a much lower energy than the T.S. for a concerted rxn.

			Futhermore, the mirror plane of symmetry, m₁, is now not present and so the reaction becomes symmetry allowed. (Work this out for yourself.) c. An idealized potential energy surface for the reac- tion looks like this (the energy units are arbitary):



	i) Although formation of the diradical will certainly be a very endothermic reaction, once it is formed it can "wander around". ii) Large regions of space spanning q₁. q_2, q₃ are extremely flat. This is called a twixtyI surface.



	iii) It seems reasonable that the diradical would be formed via:


	iv) Therefore, there are three mechanistic possibilities for this reaction:



			As pointed out earlier, there is good theoretical evi- dence that a concerted, synchronous, (where both C-C s bonds are formed at the same rate) is not possible. But this does not exclude a concerted , asynchronous path where the bonds form at different rates from one where there is a discrete tetramethylene intermediate. d. The experimental evidence for this route comes from direct observation of what is most likely the diradical intermediate by femtosecond spectroscopy.



			See Science, 266, 1359 (1994). The experimental set-up is given by two lasers: one beam is used to irradiate the molecular beam of cyclopentanone. This under- goes a very well-known decarbonylation process, called the Norrish-type a-cleavage, to produce CO, cyclobutane and ethylene. The other laser ionizes the species produced which then are mass-selected using a mass spectrometer. What comes out from this experi- ment is then a series of mass spectra of the species separated by femtoseconds. For this case of cyclopentanone ones sees:





	Notice that the peak associated with the cyclopentanone (84 amu) dies out quickly with the production of a new peak at 56 amu which is the molecular weight corresponding to tetramethylene. The kinetics associated with its production and decay is shown in part a of the figure below.



	The buildup time is t₁ = 150 ± 30 fs and the decay time is t₂ = 700 ± 40 fs for this compound. This clearly is an intermediate and not a transition state species. The precursor cyclopentanone decays with a t = 120 ± 20 fs. When cyclobutanone is used then the interme- diate species, trimethylene, has a much shorter lifetime, t₁ = t₂ = 120 ± 20 fs (see part b), whereas, stabilizing the teramethylene diradical by putting methyl substitu ents which can undergo hyperconjugation greatly increases the lifetime t₂ = 1400 ± 200 fs (see part c). Furthermore, t₂ = 190 fs for 1,3 cyclopentadiyl (why?). This is all consistent with the formation of diradical intermediates of varying lifetimes. The situation for tetramethylene is shown below. The barrier height for the diradical is estimated to be ~4 kcal/mol.


		e. Other evidence in favor of the diradical path: i) Substituents that stabilize radicals accelerate the reaction: (a) Thus for X = OR, halogen or alkyl (which stabilize radicals) dimerizations are faster.

		(b) In fact for F₂C=CF₂ the radical is so stable that polymerization is a major side reaction. ii) The regioselectivity is consistent with radicals:




		iii) The reaction is stereononselective:

		a) The diradical has a long enough lifetime to rotate freely. t_rot has been estimated to be ~200 fs - Chem Phys. Letts. 303, 249 (1999). b) The products are formed in 1:1 ratio from either set of reactants. f. Sometimes a zwitterionic intermediate is formed.


	g. Evidence for a zwitterionic pathway comes from a variety of sources: i) Hammett type substituent effects





		The very negative value of r is consistent with a zwitterion being formed so that electron density is lost from the arene (and builds up on one of the tetracyano-ethylene carbon atoms). ii) Solvent effects: in the above reaction, the rate in CH₃CN = 6.3 x 10⁴ times greater than the rate in cyclohexane. iii) The formation of intensely colored solutions charge transfer complexes


		low wavelength absorptions iv) Secondary D isotope effects:


		vi) The interception of intermediates.



		vii) A nice computational example is provided by the reaction of ketene (CH₂=C=O) with imine (CH₂=NH). In the gas phase this is a single step reaction where the C-N bond is almost fully formed and the C-C bond is quite long. If the calculations are done using a dielec- tric continuum model representing aqueous solvation, a very different picture emerges. The two paths are shown below where the numbers in parenthesis for the structures comes from the gas-phase.



		In solution a very stabile zwiterionic intermediate is formed which then must undergo rotation around the N-C bond and C-C ring closure to the product in the rate-determining step. In the gas phase this intermedi- ate is not formed. Notice that aqueous solvation appreciably stabilizes the transition state for ring closure. Geometrically there is not much difference between the two transition states. E. Olefin dimerization the photochemical reaction 1. Clues which suggest that a totally different mechanism must occur. a. A remarkable range of substituents can be used, e.g.



		b. The reaction is stereospecific, which strongly sug- gests a concerted mechanism.


	2. Let us go back to the original correlation diagram that we developed and consider what would happen in the first excited state:




	a. Excitation of an electron from the SA orbital which is strongly antibonding between the ethylenes to the AS orbital which is strongly bonding between the ethylenes, consequently will allow the olefins to ap- proach each other. This is called the exciplex. There is a neat experimental example of this phenomena on the next page which is derived from a series of very fanciful molecules, called pagodanes - see Pure and Applied Chem. 67, 673 (1995). Oxidation of the bis- olefin causes the C=C bonds to stretch by approxi- mately 0.10Å and a collapse of the non-bonded C--C distances between the two olefins by 0.55Å. Notice that oxidation of the totally saturated pagodane by two electrons also leads to the same intermediate. Here the metrical changes are opposite in sign but nearly the same in magnitude.





		b. The reaction between the first excited state of the olefin dimer and the first excited state of the cyclobutane is symmetry allowed! c. There is one problem, however, with this scheme. i) Notice that the one electron in SA must rise up very high in energy to the s* level. This should energetically be very unfavorable. ii) Another way to put this is that the 1^st excited state of an olefin lies in the UV range ( > 165 nm absorp- tion); the 1^st excited state of an alkane (s s* ~ 135nm ) is much higher. iii) There then should be no driving force for this reaction since the exciplex can return back (by flores- cence) to ground state olefin dimer. d. There is a way around this, but we have to look at the properties of the electronic state in a molecule: Y ^y_l^y₂ a product function of orbitals i) There is a symmetry associated with each state, this can be determined by multiplying each orbital function times another according to the following rules: S x S = S S x A = A A x A = S



	ii) Thus the first few excited states of the olefin dimer and cyclobutane are the following: (a) For the olefin dimer:

				this is the ground state of cyclobutane


	(b) for cyclobutane:

				this is the ground state of the olefin dimer


	iii) One can then energetically order the relative energies for the ground and excited electronic states of the olefin dimer and cyclobutane. It is now im- perative to correlate states of the same symmetry. The hypothetical scheme then is:




			conical intersection
		(a) The ground state of reactant should correlate directly (dashed line) to the doubly excited state of product and viceversa. (b) However, these two states have the same total symmetry so they avoid each other (solid line). (c) In the thermal concerted addition, this then is the source of the gigantic barrier, one goes from P to U directly via the high energy T. (d) In the photochemical process one has photochemi- cal excitation from P to Q. (i) Q must then rise in energy and at sometime (point R) cross states from AA to SS. (ii) This then immediately decays from R to S and S to T to U without activation the state symmetry always remains SS. e. But how can we test this mechanism? i) So far no one has been able to do this



	ii) The problem is that no activation energies can be measured. (a) We would expect that the crossing from Q to R (and perhaps from S to T) would have a large negative DS from related state crossings in thermal reactions. (b) The diagram is simplified in that we have not shown vibrational levels, excitation to Q does not produce Q in the first vibrational level. (c) If you look closely at the relative phases of the MO's, Q should have a C-C equilibrium distance far shorter than point P. The equilibrium distance for the doubly excited state should be even less. (d) The only thing that holds the SS ground state together is being caught in the solvent cage. Since there are no strong interactions between two ethyl- enes or solventethylene dimer, point P should be in a very shallow well. (e) An idealized onedimensional P. E. surface for the concerted reaction, redrawn according to the consid- erations above, is given below.
		conical intersection



			(i) Note: vertical excitation from P to Q produces a vibrationally excited state Q which can decay via R in any number of places without any DHcontribution. (ii) The equilibrium distance for the doubly excited SS state is actually point S halfway between reactants and products. This decays to T from the conical inter- section of the two surfaces. f. In general the potential energy surface of a photo- chemical process can be represented by:

				This is a representation of two competing thermal and photochemical processes. In the photochemical world life is much more difficult due to surface crossings, internal conversion, conical intersections and the like! i) One might think that the photochemistry of H₂ + D₂ should follow the olefin dimerization since there is a relationship between the two thermal processes. Unfortunately this is not the case. ii) The potential energy surface for the lowest doubly excited state of the H₂ + H₂ reaction is shown on the next page. It is strongly repulsive in all directions. In fact the H₂ distances are quite long compared to the ground state (see previous PE surfaces). The surface for the lowest singly excited state is shown by two views on the next page.




				This is the lowest doubly excited state


				Here are two views of the lowest singly excited state



		iii)Notice that there is a low energy cell formed. This is the exciplex. The exciplex is a square of ~1.5Å dimensions. This can be compared to H₂ in the ground state where the H-H distance is 0.74Å. F. The Diels-Alder reaction. This reaction dates back to O. Diels and K Alder, J. Liebig's Ann. Chem., 460, 98 (1928)! The parent reaction is:


		This was reported by L. Joshel and L. W. Butz, J. Am. Chem. Soc., 63, 3350 (1941). This has been a reaction which has been around for a long time. It is very useful because it is a very stereospecific reaction which tolerates many functional groups and so it is extensively used to build larger cyclic molecules from to acyclic pieces. 1. There are again three basic paths that one can consider for the reaction:


		2. Since the reaction is stereospecific, the nonconcerted path seems rather unlikely. However, an argument devel- oped for the two possible variants of the concerted reaction between two physical organic chemists, M.J.S. Dewar and Ken Houk.



	3. The first proposal of a reaction mechanism was given by Wasserman in 1935. He envisioned a concerted reaction with C-C bond distances of 2.0Å in the transition state. A early theoretical treatment of this reaction was given by Evans and Warhurst in 1938 who also predicted a con- certed process with activation barrier of 36 kcal/mol. Experimentally the reaction proceeds with a barrier of 27.5 kcal/mol and it is exothermic (DH) by 38.4 kcal/mol. 4. In more modern times, R. B. Woodward and T. J. Katz proposed that the reaction was asynchronous concerted and Dewar at the time (1959) argued strongly that it was a concerted synchronous path. Woodward and R. Hoffmann proposed a set of orbital symmetry rules in 1965 and on this basis a concerted synchronous path for the Diels-Alder reaction was preferred. On the basis of MO calculations and some philosophical discourse, Dewar in 1974 reversed himself and argued very strongly for the asynchronous path! In fact in 1984 he proclaimed in the title of a JACS article "Multibond Reactions Cannot Normally Be Synchronous". In 1986 it became recognized that there were in fact two transition states for this reaction that could be located. This was work done in Ken Houk's group who was a former student of R. B. Woodward. A very interesting, humorous account of the history of this, as well as, related mechanistic arguments can be found in Acct. Chem. 28, 81 (1995). Please get a copy and read it. 5. At the best level of theory the concerted synchronous transition state has an activation barrier of 29 kcal/mol and is 5 -7 kcal/mol lower in energy than the asychronous one. The structures are shown below



			6. Now, that estimate of the energy differences has stood the test of several more advanced computational tech- niques, however, that is not to say that the situation could not change in the future. An independent measure is derived from the computed and experiment values of secondary D-isotope effects.



			The clear pattern is that the synchronous path is closer to experiment 7. The femtosecond spectroscopy of Zewail was used to study the retro Diels-Alder reaction. See J. Am. Chem. Soc., 118, 8755 (1996). The reactions studied were the decom- position of norbornene and norboradiene.



		8. The results are shown below. Let us only consider the results for norbornene; those for norbornadiene are very similar. A species with the molecular weight of the precursor (94 amu) rises and decays with a time constant of 160 ± 20 fs. There is another species at 66 amu which rises with a time constant of 30 ± 5 fs and decays at 220 ± 20 fs. This is a real intermediate since its intensity drops off with time and it has the same molecular weight as cyclopentadiene. A careful analysis was made of the decay of the 94 amu peak and the rise of the 66 amu peak. They do not match and in fact differ by a factor of 5. Therefore, the 94 and 66 amu peaks must represent separate trajectories (reaction paths).

			9. The interpretation of these results was initially thought to be that there were two reaction paths, a concerted path leads to the species decaying with the 220 fs rate since the time constant for stretching a C-C bond is ~40 fs and, therefore, this is exactly in the range of the



		30 fs buildup. So this is then a concerted asynchronous route. The species with the 160 fs lifetime is a diradical intermediate. This is certainly a novel mecha- nism. Later MO calculations were reported by Houk et. al. - Pure App. Chem. 70, 1947 (1998) - which offered an alternative explanation. The initial photon pulse produces a highly vibrationally excited state where one electron has been promoted from the p to the p* orbital. This then decays into a conical intersection. Either one bond breaks to produce a diradical inter- mediate which then undergoes closure to form a variety of products. Alternatively two bonds are broken to form excited state cyclopentadiene which then decays. The full scheme is shown below.


		10. The moral of this story, at this point in time, is then that the femtosecond spectroscopy study of this reaction does not correlate with what occurs in the ground state thermal reaction. For most Diels-Alder reactions the synchronous concerted path is the most reasonable.



		G. This is only a very small part of the story about cycloaddition reactions. 1. Basically one must always deal with a spectrum of mechanistic behvior:

	2. What makes cycloaddition reactions so useful and a study of their mechanisms so important is that the stere- ochemistry - including regiochemistry (see below) - can be predicted and used to form much larger organic molecules.

	In other words cycloadditions form an important tool to synthesize natural products, etc. But you will have to take a couple more organic classes - physical organic and synthesis - to learn about this!