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

Houk and Doubleday have a nice follow-up study¹ to their previous MD study² of 1,3-dipolar cycloadditions, which I posted on here. They report on the cycloaddition of either acetylene or ethylene to 9 different 1,3-dipoles. Continuing on Houk’s recent thread of looking at distortion energies to attain the TS, they note that a sizable fraction (often over 50%) of the distortion energy is associated with bending the X-Y-Z bond of the dipole, consistent with their earlier work suggesting the importance of this vibration in attaining and crossing the TS. What’s new in this paper is the extensive MD studies, with trajectory studies of all 18 reactions. These revealed again the importance of vibrational energy in this X-Y-Z bending mode in crossing the TS. They also noted the role of translational energy, and the relationship between translational vs. vibrational energy depending on the early/late nature of the TS. Their final point was that the lifetime of any diradical or diradical-like intermediate is so short, less than the time of a bond vibration, so that one can discount any diradical participation. The reaction is concerted.

References

(1) Xu, L.; Doubleday, C. E.; Houk, K. N., "Dynamics of 1,3-Dipolar Cycloadditions: Energy Partitioning of Reactants and Quantitation of Synchronicity," J. Am. Chem. Soc., 2010, ASAP, DOI: /10.1021/ja909372f

(2) Xu, L.; Doubleday, C. E.; Houk, K. N., "Dynamics of 1,3-Dipolar Cycloaddition Reactions of Diazonium Betaines to Acetylene and Ethylene: Bending Vibrations Facilitate Reaction," Angew. Chem. Int. Ed., 2009, 48, 2746-2748, DOI: 10.1002/anie.200805906

One more study of cyclodiene reactions with ketenes that suggest the occurrence of dynamic effects.¹ The reaction of cyclopentadiene with t-butylcyanoketene 1 gives cyclobutanone 2 solely. In contrast, the reaction of 1,3-cyclophexadiene with 1 gives the cyclobutanone 3 and a small amount (less than 25%) of the ether 4. Warming the reaction from -20 °C to 20 °C leads to loss of 3 and an increase in 4. This is in distinct contrast with the reaction of cyclopentadiene with diphenylketene,² where the ether product is the major product and the cyclobutenone is the minor product (see Chapter 7.3.5.2 in my book).

To help understand this situation, the authors optimized the structures of the critical points on the surface of the cyclohexadiene reaction at MPWB1K/6-31+G(d,p) – though once again, there are no supporting materials so I cannot supply the 3-D structures in the blog! 4 is predicted to be 3.4 kcal mol^-1 more stable than 3, which accounts for it being the thermodynamic product, consistent with experiment. Only two transition states are found. The first TS, with a barrier of 23.2 kcal mol^-1, connects reactants with 3. The second transition state corresponds to the oxy-Cope rearrangement that takes 3 into 4. This surface is reminiscent of many others that display dynamic effects (again see my book and also these posts). Unfortunately, the authors have not performed any trajectory calculation. But one might expect that most trajectories cross the first transition state and fall into the well associated with 3. Some of these molecules then go on to cross the second barrier to form 4. But some trajectories cross the first TS and then veer off into the slightly lower well associated with 4, being directly formed from reactant. This would be a manifestation of dynamic effects, and is worth further study.

References

(1) Marton, A.; Pârvulescu, L.; Draghici, C.; Varga, R. A.; Gheorghiu, M. D., "Reaction of Moore’s ketene (tert-butylcyanoketene) with 1,3-cyclopentadiene and 1,3-cyclohexadiene. Is periselectivity controlled by the dynamic of trajectories at the bifurcation point?," Tetrahedron, 2009, 65, 7504-7509, DOI: 10.1016/j.tet.2009.07.020.

(2) Ussing, B. R.; Hang, C.; Singleton, D. A., "Dynamic Effects on the Periselectivity, Rate, Isotope Effects, and Mechanism of Cycloadditions of Ketenes with Cyclopentadiene," J. Am. Chem. Soc., 2006, 128, 7594-7607, DOI: 10.1021/ja0606024.

A nice follow-up to some of my own work points out again the possible dramatic role of dynamic effects. Way back when, Jack Gilbert discovered that the reaction of cyclopentyne with alkenes gives the cyclobutene product with stereoretention (Reaction 1),¹ seemingly in violation of the Woodward-Hoffmann rules.

Jack and I proposed an intermediate spirocyclopropyl carbene which could then open to product, and this would follow a stereoretention path.^2,3 In a subsequent paper,⁴ we noted that a diradical pathway is also possible, and conjectured that dynamics might account for the stereoretention – that formation of the diradical leads directly to the carbene, leaving a very short lifetime of the diradical (Scheme 1). The consequence of the short lived diradical is that there little opportunity to rotate about the C-C bond and scramble the stereochemistry.

Scheme 1

Pilling has published a MD study of this system and finds what we predicted.⁵ The short-time trajectories lead to stereoretention product. This is due to both passages over the TS that lead from the diradical to the product (with no scrambling) and over the TS that connects the diradical to the carbine. Longer trajectories do exhibit some stereoscrambling. Carpenter⁶ has argued that short time dynamics are often what one observes for potential energy surfaces like this one. Pilling also argues that in solution, with the actual alkene which bears bulky substituents that the proton (he examined the reaction of cyclopentyne with ethene), rotations will be slower, leading to formation of the carbene with stereoretention.

References

(1) Gilbert, J. C.; Baze, M. E., "Stereochemistry of [2 + 2] cycloadditions of cyclopentyne," J. Am. Chem. Soc. 2002, 106, 1885-1886, DOI: 10.1021/ja00318a081

(2) Laird, D. W.; Gilbert, J. C., "Norbornyne: A Cycloalkyne Reacting Like A Dicarbene," J. Am. Chem. Soc., 2001, 123, 6704-6705, DOI: 10.1021/ja010589h

(3) Bachrach, S. M.; Gilbert, J. C.; Laird, D. W., "DFT Study of the Cycloaddition Reactions of Strained Alkynes," J. Am. Chem. Soc., 2001, 123, 6706-6707, DOI: 10.1021/ja010590g

(4) Bachrach, S. M.; Gilbert, J. C., "The Reaction of Cyclopentyne with Ethene: Concerted vs Stepwise Mechanism?," J. Org. Chem., 2004, 69, 6357-6364, DOI: 10.1021/jo0492970

(5) Glowacki, D. R.; Marsden, S. P.; Pilling, M. J., "Significance of Nonstatistical Dynamics in Organic Reaction Mechanisms: Time-Dependent Stereoselectivity in Cyclopentyne−Alkene Cycloadditions," J. Am. Chem. Soc. 2009, 131, 13896-13897, DOI: 10.1021/ja9043054

(6) Barry, K. C., "Nonexponential decay of reactive intermediates: new challenges for spectroscopic observation, kinetic modeling and mechanistic interpretation," J. Phys. Org. Chem., 2003, 16, 858-868, DOI: 10.1002/poc.672

Unusual potential energy surfaces are a theme of this blog and my book (see chapter 7). Examples might include bifurcations and valley inflection points and often lead to unusual dynamics. Tantillo has now reported a bifurcation on the PES for terpene synthesis, specifically the pathway for synthesis of abietadiene.¹

Tantillo discusses two possible cation rearrangement pathways. The first is pretty ordinary, but in the second, the precursor cation 1 can rearrange through either of two transition states 2a or 2b (Scheme 1). The IRC computation from 2a connects back to 1, but in the forward direction it connects to another transition state 3. This TS (3) connects products 4 and 5. These structures are drawn in Figure 1.

Thus, the potential energy surface displays a bifurcation, and one might expect unusual dynamic effects to operate.

Scheme 1

2a	2b
3

Figure 1. B3LYP/6-31+G(d,p) optimized transition structures of 2-3.¹

References

(1) Hong, Y. J.; Tantillo, D. J., "A potential energy surface bifurcation in terpene biosynthesis," Nature Chem. 2009, 1, 384-389 DOI: 10.1038/nchem.287.

A computational study of addition of singlet carbenes to bicyclobutanes reveals another potential energy surface where dynamics may be active. Rablen, Jones and co-workers examined the reaction of dichlorocarbene with bicyclobutane 1 and 1,2,2-trimethylbicyclobutane 2 (Reactions 1 and 2) using a number of computational techniques.¹

For reaction 1, they identified three reaction pathways. The first two involve the carbene approaching along the central C-C bond. Path A (Scheme 1) involves a single transition state that leads to product 3, with a barrier of 8.4 kcal mol^-1. The second pat (pathway B), leads to critical point 4, which is a transition state at HF/6-31G* and QCISD/6-31G* but is a local minimum at CCSD/6-31G*. This minimum however is very shallow, and vibrational energy will exceed the barriers about it. Both pathways indicate an asynchronous but concerted reaction. The last pathway (C) is for insertion of the carbine into the bridgehead C-C bond, leading to the bicyclo product 5. This barrier is very high, 27 kcal mol^-1, and so this path is unlikely to be competitive.

Experimental study of Reaction 2 showed that only 6 is produced.² Rablen and Jones identified six pathways where the carbene attacks 2 along the bridgehead bond (analogous to Paths A and B, except there are three rotamers and the attack can be at either bridgehead carbon) and the insertion path that leads to 8. Once again, this last pathway has a very large barrier and is non-competitive. Attack at the unsubstituted bridgehead carbons is favored over attack at the methyl-substituted bridgehead by 2-3 kcal mol^-1. The path that leads directly to 7 has a slightly lower barrier (0.4 kcal mol^-1) than the path that leads directly to 8. The analog of Path B leads here to a true intermediate 9 through a barrier 0.4 kcal mol^-1 higher than the barrier that leads to 7. This intermediate is shown in Figure 1.

Figure 1. CCSD/6-31G* structure of intermediate 9.¹

The energies of the barriers suggest that 7 will be the major product, but not the exclusive product. Rablen and Jones point out that intermediate 9 lies in a very shallow plateau and exit from this intermediate can lead to either 7 or 8. This sort of potential energy surface has been implicated in reactions that exhibit non-statistical behavior indicative of dynamic effects (see Chapter 7 of my book). Rablen and Jones speculate that dynamics might be dictating the product distribution in Reaction 2 as well. Confirmation awaits a molecular dynamics study.

References

(1) Rablen, P. R.; Paiz, A. A.; Thuronyi, B. W.; Jones, M., "Computational Investigation of the Mechanism of Addition of Singlet Carbenes to Bicyclobutanes," J. Org. Chem. 2009, DOI: 10.1021/jo900485z

(2) Jackson, J. E.; Mock, G. B.; Tetef, M. L.; Zheng, G.-x.; Jones, M., "Reactions of carbenes with bicyclobutanes and quadricyclane : Cycloadditions with two σ bonds," Tetrahedron 1985, 41, 1453-1464, DOI: 10.1016/S0040-4020(01)96386-0.

InChIs

1: InChI=1/C4H6/c1-3-2-4(1)3/h3-4H,1-2H2
InChIKey=LASLVGACQUUOEB-UHFFFAOYAV

2: InChI=1/C7H12/c1-6(2)5-4-7(5,6)3/h5H,4H2,1-3H3
InChIKey=GJMVYBBYZUWWLJ-UHFFFAOYAI

3: InChI=1/C5H6Cl2/c1-2-3-4-5(6)7/h2,4H,1,3H2
InChIKey=FGUOQAVVVDPABB-UHFFFAOYAR

5: InChI=1/C5H6Cl2/c6-5(7)3-1-4(5)2-3/h3-4H,1-2H2
InChIKey=SUZACPSWEYRCBD-UHFFFAOYAW

6: InChI=1/C8H12Cl2/c1-6(2)8(3,4)5-7(9)10/h5H,1H2,2-4H3
InChIKey=QIFFCMZJZYIIBA-UHFFFAOYAZ

7: InChI=1/C8H12Cl2/c1-6(2)7(3)4-5-8(9)10/h5H,4H2,1-3H3
InChIKey=MOELQSRRCNAPQV-UHFFFAOYAX

8: InChI=1/C8H12Cl2/c1-6(2)5-4-7(6,3)8(5,9)10/h5H,4H2,1-3H3
InChIKey=PRCOWYZGJRWGOB-UHFFFAOYAP

The importance of dynamics in simple reactions is made yet again in a recent study by Doubleday and Houk in 1,3-dipolar cycloadditions.¹ They looked at the reaction of acetylene or ethylene with either nitrous oxide, diazonioazanide, or methanediazonium. The transition state for these 6 reactions all show a concerted reaction. The transition vector has three major components; (a) symmetric formation/cleavage of the two new σ bonds, (b) bending of the dipolar component, or (c) symmetric bending of the hydrogens of ethylene or acetylene.

Classical trajectories were traced from the transition state back to reactant and forward to product. In the approach of the two fragments, the dipole bend vibrates, but then after the TS, it needs to bend quickly to close the 5-member ring. This means that the bending mode effectively has to “turn a corner” in phase space, and without energy in this mode, the molecules will simple bounce off of each other. Analysis of the reactants indicates significant vibrational excitation of the dipole bending mode.

References

(1) Xu, L.; Doubleday, C. E.; Houk, K. N., "Dynamics of 1,3-Dipolar Cycloaddition Reactions of Diazonium Betaines to Acetylene and Ethylene: Bending Vibrations Facilitate Reaction," Angew. Chem. Int. Ed. 2009, 48, 2746-2748, DOI: 10.1002/anie.200805906

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.

Sheppard and Acevedo¹ have reported a careful re-examination of the ene reaction of singlet oxygen with alkenes that points out inherent difficulties in examining high-dimension potential energy surfaces by reducing the dimensionality.

Their work begins by careful reassessment of the computational study of Singleton, Foote and Houk.² These authors looked at the reaction of singlet oxygen with cis-2-butene by creating a 15×15 gird of optimized geometries holding the C-O distance fixed to specific values while letting the other geometric variables completely relax (see 1). These geometries were obtained at B3LYP/6-31G* and single-point energies were then obtained at CCSD(T)/6-31G*. They find two transiti0n states, one corresponding to symmetric addition of oxygen to the alkene 2 which leads to the pereperoxide 3. However, this pereperoxide 3 is not an intermediate, but rather a transition state for interconversion of the ene products 4 and 5. These structures and mechanism appear consistent with the experimental kinetic isotope effects. The authors characterize the reaction as “two-step no-intermediate”. Essentially, the reactants would cross the first transition state 1, encounter a valley-ridge inflection point that bifurcates reaction paths that go to either 3 or 4 and avoid ever reaching the second transition state 2.

Sheppard and Acevedo¹ tackle two major issues with this work. First, they are concerned about the role of solvent and so perform QM/MM computations with either DMSO, water of cyclohexane as solvent. The second factor is the choice of scanning just a 2-D grid as a projection of the multidimensional potential energy surface. Sheppard and Acevedo point out that since all other variable are optimized in this process, the hydrogen atom that is involved in the ene process must be bonded to either C or O and is therefore removed from the reaction coordinate. So they have performed a 3-D grid search where in addition to the two C-O distances they use the O-C-C angle as a variable. They find that this PES provides the more traditional stepwise pathway: a transition state that leads to formation of the pereperoxide intermediate and then a second transition state that leads to the ene product. In addition, solvent effects are significant, a not unexpected result given the large dipole of the pereperoxide.

But the main point here is that one must be very careful in reducing the dimensionality of the hypersurface and drawing conclusions from this reduced surface. It appears that the valley-ridge inflection point in the single oxygen ene reaction is an artifact of just this reduced dimensionality.

References

(1) Sheppard, A. N.; Acevedo, O., “Multidimensional Exploration of Valley-Ridge Inflection Points on Potential-Energy Surfaces,” J. Am. Chem. Soc. 2009, 131, 2530-2540, DOI: 10.1021/ja803879k.

(2) Singleton, D. A.; Hang, C.; Szymanski, M. J.; Meyer, M. P.; Leach, A. G.; Kuwata, K. T.; Chen, J. S.; Greer, A.; Foote, C. S.; Houk, K. N., “Mechanism of Ene Reactions of Singlet Oxygen. A Two-Step No-Intermediate Mechanism,” J. Am. Chem. Soc. 2003, 125, 1319-1328, DOI: 10.1021/ja027225p.

InChIs

Pereperoxide: InChI=1/C4H9O2/c1-3-4(2)6(3)5/h3-5H,1-2H3/t3-,4+
InChIKey=FRFPREFIPHRMOI-ZXZARUISBV

3: InChI=1/C4H8O2/c1-3-4(2)6-5/h3-5H,1H2,2H3/t4-/m1/s1
InChIKey=KRKIWMRTOODQMQ-SCSAIBSYBR

4: InChI=1/C4H8O2/c1-3-4(2)6-5/h3-5H,1H2,2H3/t4-/m0/s1
InChIKey=KRKIWMRTOODQMQ-BYPYZUCNBC

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