Dynamic effects rear up yet again in a seemingly simple reaction. Singleton has examined the Diels-Alder cycloaddition of acrolein with methyl vinyl ketone to give two cross products 1 and 2.¹ Upon heating the product mixture, 1 is essentially the only observed species. The retro-Diels-Alder is much slower than the conversion of 2 into 1. Using a variety of rate data, the best estimate for the relative formation of 1:2 is 2.5.

The eight possible transition states for this reaction were computed with a variety of methodologies, all providing very similar results. The lowest energy TS is TS3. A TS of type TS4 could not be found; all attempts to optimize it collapsed to TS3.

IRC computations indicate the TS3 leads to 1. The lowest energy TS that leads to 2 is TS6, but a second TS (TS5) lower in energy than TS6 also leads to 1. The other TS are still higher in energy. A Cope-type TS that interconverts 1 and 2 (TS7) was also located. The geometries of these TSs are shown in Figure 1.

TS3 (0.0)	TS5 (4.2)
TS6 (5.2)	TS7 (-0.4)

Figure 1. MP2/6-311+G** optimized geometries and relative energies (kcal mol^-1) of TS3-TS7.¹

Ordinary transition state theory cannot explain the experimental results – the energy difference between the lowest barrier to 1 (TS3) and to 2 (TS6) suggests a rate preference of over 700:1 for 1:2. But the shape of the potential energy surface is reminiscent of others that have been discussed in both my book (Chapter 7) and this blog (see my posts on dynamics) – a surface where trajectories cross a single TS but then bifurcate into two product wells.

To address the chemical selectivity on a surface like this, one must resort to molecular dynamics and examine trajectories. In their MD study of the 296 trajectories that begin at TS3 with motion towards product, 89 end at 1 and 33 end at 2, an amazingly good reproduction of experimental results! Interestingly, 174 trajectories recross the transition state and head back towards reactants. These recrossing trajectories result from “bouncing off” the potential energy wall of the forming C₄-C₅ bond.

In previous work, selectivity in on these types of surfaces was argued in terms of which well the TS was closer to. But analysis of the trajectories in this case revealed that a strong correlation exists between the initial direction and velocity in the 98 cm^-1 vibration – the vibration that corresponds to the closing of the second σ bond, the one between C₆-O₁ (forming 1), in the negative direction, and closing the C­₃-O₈ bond (forming 2) in the positive direction. Singleton argues that this is a type of dynamic matching, and it might be more prevalent that previously recognized.

References

(1) Wang, Z.; Hirschi, J. S.; Singleton, D. A., "Recrossing and Dynamic Matching Effects on Selectivity in a Diels-Alder Reaction," Angew. Chem. Int. Ed., 2009, 48, 9156-9159, DOI: 10.1002/anie.200903293

InChIs

1: InChI=1/C7H10O2/c1-6(8)7-4-2-3-5-9-7/h3,5,7H,2,4H2,1H3
InChIKey=AOFHZPHBPUYLAG-UHFFFAOYAJ

2: InChI=1/C7H10O2/c1-6-3-2-4-7(5-8)9-6/h3,5,7H,2,4H2,1H3
InChIKey=PLZQHPPETMMEED-UHFFFAOYAD

Singleton has again found a great example of a simple reaction that displays unmistakable non-statistical behavior.¹ The hydroboration of terminal alkenes proceeds with selectivity, preferentially giving the anti-Markovnikov product. The explanation for this selectivity is given in all entry-level organic textbooks – who would think that such a simple reaction could in fact be extraordinarily complex?

Reaction 1, designed to minimize the role of hydroboration involving higher order boron-hydrides (RBH₂ and R₂BH), the ratio of anti-Markovnikov to Markovinkov product is 90:10. Assuming that this ratio derives from the difference in the transition state energies leading to the two products, using transition state theory gives an estimate of the energy difference of the two activation barriers of 1.1 to 1.3 kcal mol^-1.

The CCSD(T)/aug-cc-pVDZ optimized structures of the precomplex between BH₃ and propene 1, along with the anti-Markovnikov transition state 2 and the Markovnikov transition state 3 are shown in Figure 2. The CCSD(T) energy extrapolated for infinite basis sets and corrected for enthalpy indicate that the difference between 2 and 3 is 2.5 kcal mol^-1. Therefore, transiitn state theory using this energy difference predicts a much greater selectivity of the anti-Markovnikov product, of about 99:1, than is observed.

1
2	3

Figure 1. CCSD(T)/aug-cc-pVDZ optimized geometries of 1-3.¹

In the gas phase, formation of the precomplex is exothermic and enthalpically barrierless. (A free energy barrier for forming the complex exists in the gas phase.) When a single THF molecule is included in the computations, the precomplex is formed after passing through a barrier much higher than the energy difference between 1 and either of the two transition states 2 or 3. (2 is only 0.8 kcal mol^-1 above 1 in terms of free energy.) So, Singleton speculated that there would be little residence time within the basin associated with 1 and the reaction might express non-statistical behavior.

Classical trajectories were computed. When trajectories were started at the precomplex 1, only 1% led to the Markovnikov product, consistent with transition state theory, but inconsistent with experiment. When trajectories were initiated at the free energy transition state for formation of the complex (either with our without a single complexed THF), 10% of the trajectories ended up at the Markovnikov product, as Singleton put it “fitting strikingly well with experiment”!

Hydroboration does not follow the textbook mechanism which relies on transition state theory. Rather, the reaction is under dynamic control. This new picture is in fact much more consistent with other experimental observations, like little change in selectivity with varying alkene substitution² and the very small H/D isotope effect of 1.18.³ Singleton adds another interesting experimental fact that does not jibe with the classical mechanism: the selectivity is little affect by temperature, showing 10% Markovnikov product at 21 °C and 11.2% Markovnikov product at 70 °C. Dynamic effect rears its ugly complication again!

References

(1) Oyola, Y.; Singleton, D. A., “Dynamics and the Failure of Transition State Theory in Alkene Hydroboration,” J. Am. Chem. Soc. 2009, 131, 3130-3131, DOI: 10.1021/ja807666d.

(2) Brown, H. C.; Moerikofer, A. W., “Hydroboration. XV. The Influence of Structure on the Relative Rates of Hydroboration of Representative Unsaturated Hydrocarbons with Diborane and with Bis-(3-methyl-2-butyl)-borane,” J. Am. Chem. Soc. 1963, 85, 2063-2065, DOI: 10.1021/ja00897a008.

(3) Pasto, D. J.; Lepeska, B.; Cheng, T. C., “Transfer reactions involving boron. XXIV. Measurement of the kinetics and activation parameters for the hydroboration of tetramethylethylene and measurement of isotope effects in the hydroboration of alkenes,” J. Am. Chem. Soc. 1972, 94, 6083-6090, DOI: 10.1021/ja00772a024.

Singleton has taken another foray into the murky arena of “dynamic effects”, this time with the aim of trying to provide some guidance towards making qualitative product predictions.¹ He has examined four different Diels-Alder reaction involving two diene species, each of which can act as either the diene or dienophile. I will discuss the results of two of these reactions, namely the reactions of 1 with 2 (Reaction 1) and 1 with 3 (Reaction 2).

In the experimental studies, Reaction 1 yields only 4, while reaction 2 yields both products in the ratio 6:7 = 1.6:1. Standard transition state theory would suggest that there are two different transition states for each reaction, one corresponding to the 4+2 reaction where 1 is the dienophile and the other TS has 1 as the dienophile. Then one would argue that in Reaction 1, the TS leading to 4 is much lower in energy than that leading to 5, and for Reaction 2, the TS state leading to 6 lies somewhat lower in energy than that leading to 7.

Now the interesting aspect of the potential energy surfaces for these two reactions is that there are only two transition states. The first corresponds to the Cope rearrangement between the two products (connecting 4 to 5 on the PES of Reaction 1 and 6 to 7 on the PES of Reaction 2). That leaves only one TS connecting reactants to products! These four TSs are displayed in Figure 1.

Reaction 1	Reaction 2
TS 12→45	TS 13→67
Cope TS 4→5	Cope TS 6→7

Figure 1. MPW1K/6-31+G** TSs on the PES of Reactions 1 and 2.¹

These transition states are “bispericyclic” (first recognized by Caramella²), having the characteristics of both possible Diels-Alder reactions, i.e. for Reaction 1 these are the [4π₁+2π₂] and [4π₂+2π₁]. What this implies is that the reactants come together, cross over a single transition states and then pass over a bifurcating surface where the lowest energy path (the IRC or reaction path) continues on to one product only. The second product, however, can be reached by passing over this same transition state and then following some other non-reaction path. This sort of surface is ripe for experiencing non-statistical behavior, or “dynamic effects”.

Trajectory studies were then performed to explore the product distributions. Starting from TS 12→45, 39 trajectories were followed: 28 ended with 4 and 10 ended with 5 while one trajectory recrossed the transition state. Isomerization of 5 into 4 is possible, and the predicted low barrier for this explains the sole observation of 4. For Reaction 2, of the 33 trajectories that originated at TS 13→67, 12 led to 6 and 19 led to 7. This distribution is consistent with the experimental product distribution of a slight excess of 7 over 6.

Once again we see here a relatively simple reaction whose product distribution is only interpretable using expensive trajectory computations, and the result leave little simplifying concepts to guide us in generalizing to other (related) systems. Singleton does provide two rules-of-thumb that may help prod us towards creating some sort of dynamic model. First, he notes that the geometry of the single transition state that “leads” to the two products can suggest the major product. The TS geometry can be “closer” to one product over the other. For example, in TS 12→45 the two forming C-C bonds that differentiate the two products are 2.95 and 2.99 Å, and the shorter distance corresponds to forming 4. In TS 13→67, the two C-C distances are 2.83 and 3.13 Å, with the shorter distance corresponding to forming 6. The second point has to do with the position of the second TS, the one separating the two products. This TS acts to separate the PES into two basins, one for each product. The farther this TS is from the first TS, the greater the selectivity.

As Singleton notes, neither of these points is particularly surprising in hindsight. Nonetheless, since we have so little guidance in understanding reactions that are under dynamic control, any progress here is important.

References

(1) Thomas, J. B.; Waas, J. R.; Harmata, M.; Singleton, D. A., "Control Elements in Dynamically Determined Selectivity on a Bifurcating Surface," J. Am. Chem. Soc. 2008, 130, 14544-14555, DOI: 10.1021/ja802577v.

(2) Caramella, P.; Quadrelli, P.; Toma, L., "An Unexpected Bispericyclic Transition Structure Leading to 4+2 and 2+4 Cycloadducts in the Endo Dimerization of Cyclopentadiene," J. Am. Chem. Soc. 2002, 124, 1130-1131, DOI: 10.1021/ja016622h

InChIs

1: InChI=1/C7H6O3/c1-10-7(9)5-2-3-6(8)4-5/h2-4H,1H3
InChIKey=XDEAUYSKQHEYSC-UHFFFAOYAM

2: InChI=1/C8H12/c1-2-8-6-4-3-5-7-8/h2,6H,1,3-5,7H2
InChIKey=SDRZFSPCVYEJTP-UHFFFAOYAI

3: InChI=1/C6H6O/c1-2-6-4-3-5-7-6/h2-5H,1H2
InChIKey=QQBUHYQVKJQAOB-UHFFFAOYAO

4: InChI=1/C15H18O3/c1-18-14(17)15-9-8-13(16)12(15)7-6-10-4-2-3-5-11(10)15/h6,8-9,11-12H,2-5,7H2,1H3/t1,12-,15+/m1/s1
InChIKey=IASNDVSMFFVIFJ-GDHFLIHABF

5: InChI=1/C15H18O3/c1-18-15(17)13-8-11-10(7-12(13)14(11)16)9-5-3-2-4-6-9/h5,8,10-12H,2-4,6-7H2,1H3
InChIKey=XOFSMKQRRVWZHS-UHFFFAOYAW

6: InChI=1/C13H12O4/c1-16-13(15)10-6-8-7(5-9(10)12(8)14)11-3-2-4-17-11/h2-4,6-9H,5H2,1H3
InChIKey=HTSLDILNKGZMHE-UHFFFAOYAH

7: InChI=1/C13H12O4/c1-16-12(15)13-6-4-10(14)8(13)2-3-11-9(13)5-7-17-11/h3-9H,2H2,1H3/t8-,9?,13-/m1/s1
InChIKey=URYPWPBQFGUBGW-KEJGKJRFBM

Well, here’s my vote for paper of the year (at least so far!). It is work from Barry Carpenter’s lab¹ and pertains to many topics discussed in my book, including pericyclic and psuedopericylic reactions, non-statistical dynamics, and the use of high-level computations to help understand confusing experimental results. The paper is in an interesting read – and not just for the great science. It is told as a story, recounting the experiments and interpretation as they took place in chronological order with a surprising and critical contribution made from a referee!

The story begins with Carpenter’s continuing interest in unusual dynamic effects and the supposition that non-statistical dynamics might be observed in the rearrangements of carbenes. So, they took on the Wolff rearrangement, specifically the rearrangement of 3 into 4. Using labeled starting material 1, one should observe equal amounts of 4a and 4b if normal statistical dynamics is occurring (Scheme 1).

Scheme 1.

In fact, the ratio of products is not unity, but rather 4a:4b = 1:4.5. But the excess of 4b could be the result of another parallel rearrangement, 2 to 5 to 4b (Scheme 2).

Scheme 2.

To try to distinguish whether 5 is intervening, they carried out the photolysis of a different labeled version of 1 (namely 1’). The product distribution of the products is shown in Sheme 3. It appears that the reaction through 5 dominates, but the ratio of products that come from 3 still shows non-statistical behavior.

Scheme 3.

CCSD(T) computation suggested that 5 is higher in energy than 3, and this does not help understand the experiments. At this point, Carpenter decided to write up the work as a communication, with the main point that non-statistical dynamics were occurring.

Now here an unusual event took place that offers up hope that the peer-review system still works! A referee, later identified as Dan Singleton, offered an alternative mechanism for the production of 5. Shown in Scheme 4 is the novel pseudopericylic reaction that leads from 1 directly to 5. In fact, the transition state for this pseudopericyclic reaction is 19.0 kcal mol^-1 lower in energy than the transition state for the retro-Diels-Alder reaction of Scheme 1 (computed at MPWB1K/ 6-31+G(d,p), and this pseudopericyclic TS is shown in Figure 1).

Scheme 4.

Figure 1. MPWB1K/6-31+G(d,p) optimized geometry of the transition state for the pseudopericyclic reaction shown in Scheme 4.¹

The revised mechanism was then modified to include the additional complication of the formation of 6, and is shown in Scheme 5, along with their relative CCSD(T) energies. The CCSD(T)/cc-pVTZ//CCSD/cc-pVTZ optimized geometries of the critical points of Scheme 5 are drawn in Figure 2.

Scheme 5.

5
TS 5 → 3	3
TS 5 → 6	6
TS 5 → 4	4

Figure 2. CCSD/cc-pVTZ optimized geometries.¹

Any non-statistical effect would occur in the transition from 5 to 3. A direct dynamics trajectory analysis was performed starting in the neighborhood of this TS using three different functionals to generate the potential energy surface. Though only 100 trajectories were computed, the results with all three functionals are similar. About 2/3rds of these trajectories led to 3 followed by the shift of the C₅ methyl group. Another 15% led to 3 and then the C₁ methyl shifted. This MD simulation supports the non-statistical Wolff rearrangement, with a clear preference for the C₅ shift, consistent with experiment. A larger MD study is underway and will hopefully shed additional insight onto this fascinating reaction.

References

(1) Litovitz, A. E.; Keresztes, I.; Carpenter, B. K., "Evidence for Nonstatistical Dynamics in the Wolff Rearrangement of a Carbene," J. Am. Chem. Soc., 2008, 130, 12085-12094, DOI: 10.1021/ja803230a.

InChIs

3: InChI=1/C5H6O2/c1-4(6)3-5(2)7/h1-2H3
InChIKey = IGYQBMPIQGLNRU-UHFFFAOYAO

4: InChI=1/C5H6O2/c1-4(3-6)5(2)7/h1-2H3
InChIKey = ABVJXABNYINQLN-UHFFFAOYAA

5: InChI=1/C5H6O2/c1-3-5(7)4(2)6/h1-2H3
InChIKey = FJJXVDYICOYKRN-UHFFFAOYAD

6: InChI=1/C5H6O2/c1-4-3(6)5(4,2)7-4/h1-2H3
InChIKey = CAMBQRQJZBTNNS-UHFFFAOYAB