Careful consideration of orbital topolologies of pericyclic reactions has led to the recent flurry of activity related to Möbius aromaticity, homoaromaticity, and antiaromaticity. I discussed this briefly in Chapter 2 of the book and in these posts (1, 2, 3). Mauksh and Tsogoeva¹ have clearly demoted the four different topologies of the transition state of pericyclic reactions. One need to be concerned about (a) the topology of the molecule (does it will have the familiar twist of a Möbius strip or not?) and (b) the topology of the π-system (is there a phase inversion or not?). These four topologies are shown in Figure 1. The pink stick represents the positive lobe of the carbon p orbital.

(A)	(B)
(C)	(D)

Figure 1. Topologies of electrocyclization reactions.

Three of these possibilities had been previously identified. The first (Fig. 1A) is the TS for the electrocyclization of 1,3,5-hexadiene. It has both Hückel topology of the molecule and the p orbitals. The second example (Fig. 1B) is the classic Zimmerman example of the electrocyclization of all-cis 1,3,5,7-octatetraene. It has Hückel topology of the molecule but one phase inversion of the p orbitals. The third example (Fig 1C) is the electrocyclization of (3E,5Z,7E)-1,3,5,7,9-decapentaene, proposed by Rzepa.² Here we have a Möbius topology but there is no phase inversion of the p orbitals.

Mauksch and Tsogoeva report on the novel electrocylization of (3E,5E,7E,9E)-1,3,5,7,9,11-dodecahexaene (1), the fourth topology type (Fig 1d).¹ Here the molecule has the Möbius topology and there is one phase inversion. Figure 2 displays the geometries of the reactant 1, the electrocyclization transition state 2, and the product 3. The activation barrier is 35.7 kcal mol^-1. The NICS value at the center of the ring of the transition state is -12.8ppm , indicative of aromatic character, which is supported by the very small variation of the C-C distances (less than 0.02 Å).

1

2

3

Figure 2. B3LYP/6-31G* optimized geometries of 1-3.¹

Henry Rzepa has commented on this paper in his blog, along with detailing another example of this type of topology. In a second post, Henry discusses the issue of competition between aromatic and antiaromatic character in a related molecule.

References

(1) Mauksch, M.; Tsogoeva, S. B., "A Preferred Disrotatory 4n Electron Möbius Aromatic Transition State for a Thermal Electrocyclic Reaction," Angew. Chem. Int. Ed., 2009, 48, 2959-2963, DOI: 10.1002/anie.200806009

(2) Rzepa, H. S., "Double-twist Möbius aromaticity in a 4n+2 electron electrocyclic reaction," Chem. Commun., 2005, 5220-5222, DOI: 10.1039/b510508k.

InChIs

(3Z)-1,3,5-hexatriene: InChI=1/C6H8/c1-3-5-6-4-2/h3-6H,1-2H2/b6-5-
InChIKey=AFVDZBIIBXWASR-WAYWQWQTBR

(3Z,5Z)-octa-1,3,5,7-tetraene: InChI=1/C8H10/c1-3-5-7-8-6-4-2/h3-8H,1-2H2/b7-5-,8-6-
InChIKey=VXQUABLSXKFKLO-SFECMWDFBK

(3Z,5E,7Z)- 1,3,5,7,9-decapentaene: InChI=1/C10H12/c1-3-5-7-9-10-8-6-4-2/h3-10H,1-2H2/b7-5-,8-6-,10-9+
InChIKey=XKWRJEBRBGIQBA-LODOGNSSBI

(3Z,5Z,7Z,9Z)- 1,3,5,7,9,11-dodecahexaene (1): InChI=1/C12H14/c1-3-5-7-9-11-12-10-8-6-4-2/h3-12H,1-2H2/b7-5-,8-6-,11-9-,12-10-
InChIKey=GLCGEJFIZRSXBL-CAVFYFSLBM

(1Z,3Z,5E,7Z,9Z)-cyclododeca-1,3,5,7,9-pentaene (3): InChI=1/C12H14/c1-2-4-6-8-10-12-11-9-7-5-3-1/h1-10H,11-12H2/b2-1+,5-3-,6-4-,9-7-,10-8-
InChIKey=DULJMQFBRDFTQN-UWFJMCQMBK

Another two benchmarking studies of the performance of DFT have appeared.

The first is an examination by Csonka and French of the ability of DFT to predict the relative energy of carbohydrate conformation energies.¹ They examined 15 conformers of α- and β-D-allopyranose, fifteen conformations of 3,6-anydro-4-O-methyl-D-galactitol and four conformers of β-D-glucopyranose. The energies were referenced against those obtained at MP2/a-cc-pVTZ(-f)//B3LYP/6-31+G*. (This unusual basis set lacks the f functions on heavy atoms and d and diffuse functions on H.) Among the many comparisons and conclusions are the following: B3LYP is not the best functional for the sugars, in fact all other tested hybrid functional did better, with MO5-2X giving the best results. They suggest the MO5-2X/6-311+G**//MO5-2x/6-31+G* is the preferred model for sugars, except for evaluating the difference between ¹C₄ and ⁴C₁ conformers, where they opt for PBE/6-31+G**.

The second, by Korth and Grimme, describes a “mindless” DFT benchmarking study.²
This is really not a “mindless” study (as the term is used by Schaefer and Schleyer³ and discussed in this post, where all searching is done in a totally automated way) but rather Grimme describes a procedure for removing biases in the test set. Selection of “artificial molecules” is made by first deciding how many atoms are to be present and what will be the distribution of elements. In their two samples, they select systems having 8 atoms. The two sets differ by the distribution of the elements. The first set the atoms Na-Cl are one-third as probable as the elements Li-F, which are one-third as probable as H. The second set has the probability distribution similar to those found in naturally occurring organic compounds. The eight atoms, randomly selected by the computer, are placed in the corners of a cube and allowed to optimize (this is reminiscent of the “mindless” procedure of Schaefer and Schleyer³). This process generates a selection of random bonding environments along with open- and closed shell species, and removes (to a large degree) the biases of previous test sets, which are often skewed towards small molecules, ones where accurate experiments are available or geared towards a select group of molecules of interest. Energies are then computed using a variety of functional and compared to the energy at CCSD(T)/CBS. The bottom line is that the functional nicely group along the rungs defined by Perdew:⁴ LDA is the poorest performer, GGA does much better, the third rung of meta-GGA functionals are slightly better than GGA functionals, hybrids do better still, and the fifth rung functionals (double hybrids) perform quite well. Also of interest is that CCSD(T)/cc-pVDZ gives quite large errors and so Grimme cautions against using this small basis set.

References

(1) Csonka, G. I.; French, A. D.; Johnson, G. P.; Stortz, C. A., "Evaluation of Density Functionals and Basis Sets for Carbohydrates," J. Chem. Theory Comput. 2009, ASAP, DOI: 10.1021/ct8004479.

(2) Korth, M.; Grimme, S., ""Mindless" DFT Benchmarking," J. Chem. Theory Comput. 2009, ASAP, DOI: 10.1021/ct800511q.

(3) Bera, P. P.; Sattelmeyer, K. W.; Saunders, M.; Schaefer, H. F.; Schleyer, P. v. R., "Mindless Chemistry," J. Phys. Chem. A 2006, 110, 4287-4290, DOI: 10.1021/jp057107z.

(4) Perdew, J. P.; Ruzsinszky, A.; Tao, J.; Staroverov, V. N.; Scuseria, G. E.; Csonka, G. I., "Prescription for the design and selection of density functional approximations: More constraint satisfaction with fewer fits," J. Chem. Phys. 2005, 123, 062201-9, DOI: 10.1063/1.1904565

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

Tetraphenylene 1 has a saddle-shape. The barrier for interconverting the two mirror image saddles has been estimated to range from about 5 kcal mol^-1 to as much as 220 kcal mol^-1. These estimates were made either experimentally, by placing a substituent on the ring and measuring the energy needed to racemize the compound or by fairly primitive computation (CNDO).

Bau, Wong and co-workers have prepared the dideutero and dimethyl derivations 2 and 3.¹ The optical activity of 2 turns out to be far too small to be useful (and the effort expended to determine if 2 is enantiopure is truly heroic). 3 proved to have significant optical activity and so could be used to determine if enantiopure 3 racemized under heating. Amazingly, there was no measurable loss of optical activity upon heating at 550 °C for 4 hours. Rather, heating at higher temperature lead to decomposition and no noticeable racemization. To corroborate this very high barrier for racemization, they optimized the structure of 1 in its ground state saddle geometry 1s and in its planar form 1p, presumably the transition state for racemization. These two geometries (B3LYP/6-31G(d,p) are shown in Figure 1. The barrier is an astounding 135.8 kcal mol^-1, consistent with the experiment.

They apparently did not perform a frequency computation to confirm that 1p is a true transition state. In fact, Müllen, Klärner, Roth and co-workers demonstrated that the transition state for the ring flip of 1 is not planar.² They located a C₁ TS using MM2 that is some 66 kcal mol^-1 above the tub-shaped ground state.

I have just published a follow up study on 1 and the related benzannulated cyclooctatetraenes.³ The true transition state for the ring flip of 1 has D₄ symmetry (1ts) and is shown in Figure 1. The barrier for ring flip through 1ts is 76.5 kcal mol^-1 at B3LYP/6-31G(d,p) (78.6 kcal mol^-1 at MP2/6-31G(d,p)). This barrier is too large to be overcome by heating, and so Bau and Wong are correct in concluding that decomposition proceeds racemization.

1	1p
1ts

Figure 1. B3LYP/6-31G(d,p) structures of 1,¹ 1p,¹ and 1ts.³

References

(1) Huang, H.; Stewart, T.; Gutmann, M.; Ohhara, T.; Niimura, N.; Li, Y.-X.; Wen, J.-F.; Bau, R.; Wong, H. N. C., “To Flip or Not To Flip? Assessing the Inversion Barrier of the Tetraphenylene Framework with Enantiopure 2,15-Dideuteriotetraphenylene and 2,7-Dimethyltetraphenylene,” J. Org. Chem. 2009, 74, 359-369, DOI: 10.1021/jo802061p.

(2) Müllen, K.; Heinz, W.; Klärner, F.-G.; Roth, W. R.; Kindermann, I.; Adamczk, O.; Wette, M.; Lex, J., “Inversionsbarrieren ortho,ortho’-verbücketer Biphenyle,” Chem. Ber. 1990, 123, 2349-2371.

(3) Bachrach, S. M., “Tetraphenylene Ring Flip Revisited,” J. Org. Chem. 2009, DOI: 10.1021/jo900413d.

InChIs

1: InChI=1/C24H16/c1-2-10-18-17(9-1)19-11-3-4-13-21(19)23-15-7-8-16-24(23)22-14-6-5-12-20(18)22/h1-16H/b19-17-,20-18-,23-21-,24-22-
InChIKey=KTQYWNARBMKMCX-LEYBOLSUBU

2: InChI=1/C24H16/c1-2-10-18-17(9-1)19-11-3-4-13-21(19)23-15-7-8-16-24(23)22-14-6-5-12-20(18)22/h1-16H/b19-17-,20-18-,23-21-,24-22-/i1D,3D
InChIKey=KTQYWNARBMKMCX-UEXWXQHBFR

3: InChI=1/C26H20/c1-17-11-13-23-24-14-12-18(2)16-26(24)22-10-6-4-8-20(22)19-7-3-5-9-21(19)25(23)15-17/h3-16H,1-2H3/b20-19-,24-23-,25-21-,26-22-
InChIKey=XIGXQJCZIXRTIQ-CURPJEMVBV