In Chapter 2.2, we suggest that the experimental deprotonation energy (DPE) of cyclohexane is in doubt. G2MP2 predicts the DPE of cyclohexane is 414.5 kcal mol^-1, a figure significantly higher than the experimental¹ value of 404 kcal mol^-1. Given that the deviation between the G2MP2 computed DPE and experiment is about 2 kcal mol^-1, we suggest that cyclohexane should be re-examined.

In a recent JACS article,² Kass calls into question the experimental bond dissociation energies (BDE) of the small cycloalkanes. With his experimental determination of the BDE of both the vinyl and allylic positions of cyclobutene, Kass can compare experimental and computed BDEs for a range of hydrocarbon environments, as listed in Table 1. The two composite methods G3 and W1 provide excellent BDE values for the small alkanes, one acyclic alkene, and the small cyclic alkenes. These composite methods appear to accurately predict BDEs of hydrocarbons.

However, the small cyclic alkanes are dramatic outliers. The well-accepted experimental BDEs of cyclopropane, cyclobutane, and cyclohexane are 3-5 kcal mol^-1 lower than those predicted by the composite methods. Given the strong performance of the computational methods, and the difficulties associated with experimental determinations of BDEs, Kass suggests that the BDEs of these cycloalkanes are in error. Further experiments are deserved.

Table 1. Computed and experimental BDEs (kcal mol-1) of some simple hydrocarbons.
	G3a	W1a	Expt.
Methane	104.2	104.3	105.0±0.1b 104.9±0.2c
Ethane	101.2	101.2	100.5±0.3b 101.1±0.4c
(CH3)CH2	98.9	98.4	98.1±0.7b 97.8±0.5c
CH3CH2CH2CH3	98.8	98.8	98.3±0.5b 98.3±0.5c
Z-2-butene (allyl)	86.0	87.0	85.6±1.5d
Cyclopropene (vinyl)	109.6	109.8	106.7±3.7e
Cyclopropene (allyl)	100.4	100.4	90.6±4.0f
Cyclobutene (vinyl)	111.9	112.4	112.5±2.5a
Cyclobutene (allyl)	90.6	91.7	91.2±2.3a
Cyclopentene (allyl)	84.2	85.0	82.3±1.1g
Cyclohexene (allyl)	83.9		85±1h
Cyclopropane	109.2	109.0	106.3±0.3b 106.3±0.3c
Cyclobutane	100.5	99.9	96.8±1.0b 96.5±1.0c
Cyclopentane	96.4	96.9	95.6±1.0b 96.4±0.6c
Cyclohexane	100.0		99.5±1.2b 95.5±1.0c
aRef. 2. bRef. 3. cRef. 4. dRef. 5. eRef. 6. fRef. 7. gRef. 8. hRef. 9

References

(1) NIST webbook, 2005, http://webbook.nist.gov/.

(2) Tian, Z.; Fattahi, A.; Lis, L.; Kass, S. R., "Cycloalkane and Cycloalkene C-H Bond Dissociation Energies," J. Am. Chem. Soc. 2006, 128, 17087-17092, DOI: 10.1021/ja065348u

(3) Yao, Y.-R. Handbook of Bond Dissociation Energies in Organic Compounds; CRC Press: Boca Raton, FL, 2003.

(4) CRC Handbook of Chemistry and Physics; 85th ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 2004.

(5) Tsang, W. In Energetics of Stable Molecules and Reactive Intermediates, NATO Science Series C; Minas da Piedade, M. E., Ed.; Kluwer Academic Publishers: Dordrecht, Netherlands, 1999; Vol. 535.

(6) Fattahi, A.; McCarthy, R. E.; Ahmad, M. R.; Kass, S. R., "Why Does Cyclopropene Have the Acidity of an Acetylene but the Bond Energy of Methane?," J. Am. Chem. Soc. 2003, 125, 11746-11750, DOI: 10.1021/ja035725s.

(7) DeFrees, D. J.; McIver, R. T., Jr.; Hehre, W. J., "Heats of Formation of Gaseous Free Radicals via Ion Cyclotron Double Resonance Spectroscopy," J. Am. Chem. Soc. 1980, 102, 3334-3338, DOI: 10.1021/ja00530a005.

(8) Furuyama, S.; Golden, D. M.; Benson, S. W., "Kinetic Study of the Gas-Phase Reaction c-C₅H₈+I₂ c-C₅H₆+2HI. Heat of Formation and the Stabilization Energy of the Cyclopentenyl Radical," Int. J. Chem. Kinet. 1970, 2, 93-99.

(9) Alfassi, Z. B.; Feldman, L., "The Kinetics of Radiation-Induced Hydrogen Abstraction
by Trichloromethyl Radicals in the Liquid Phase: Cyclohexene," Int. J. Chem. Kinet. 1981, 13, 771-783.

Addition of enolboranes to α-substituted aldehydes

In Chapter 5.2, we discussed a number of computation studies of the origins of asymmetry in 1,2-additions. We discussed the importance of the Felkin-Anh model, but that modifications of this model are needed to rationalize the broad range of addition reactions.

One modification was presented by Frenking,¹ who noted that in the addition of LiH to propanal, it was the conformation of the aldehyde that dictated the energy of the possible transition states. The lowest energy transition state is 1a, lying 1.3 kcal mol^-1 below 1b and 1.6 kcal mol^-1 below 1c (computed at MP2/6-31G(d)//HF/6-31G(d)). When the LiH fragment is removed and all other atoms kept frozen in their positions in the three transition states, 1a remains the lowest in energy.

A recent article by Cramer and Evans² examined the addition of enolboranes to aldehydes and also noted the importance of the aldehyde conformation in dictating the stereochemical outcome. The main thrust was, however, that the Cram-Conforth type model for 1,2-addition is more appropriate for some enolborane additions.

This work derives from Evans’ earlier experimental study of the addition of the boron enolate of 2-methyl-3-pentanone to a-alkoxyaldehydes (Scheme 1).³ Evans suggested that there were four transition state models that give a 3,4-anti relationship in the product (Scheme 2). The Felkin-Anh model favors B, since it avoids the syn interaction, and so E enolates will have a greater anti selectivity than Z enolates. On the other hand, the Conforth model favors transition state C, and predicts that Z enolates will have greater anti selectivity. The addition of Z enolates in fact gives large anti selectivity, while addition of E enolates gives poor anti selectivity. These results are consistent with the Cram-Cornforth model.

Scheme 1.

Scheme 2.

Cee, Cramer and Evans² examined the addition of enolborane to a number of a-substituted propanal compounds. They located six transition states (Figure 1) for the reaction of 2-fluoropropanal, three leading to the (R,S) product (2A-C) and three leading to the (S,S) product (2A’-C’). The lowest energy transition states, 2A and 2A’, both have the fluorine atom positioned anti to the carbonyl, consistent with the Cornforth model. This reflects the stability of 2-fluoropropanal. Similar results are found for addition to 2-chloropropanal

2A (0.0) xyz file		2B (2.4) xyz file
2C (2.6) xyz file
2A’ (0.8) xyz file		2B’ (1.4) xyz file
2C’ (3.7) xyz file

Figure 1. Optimized transition states and relative energies (kcal mol^-1) for the reaction of 2-fluoropropanal with enolborane computed at B3LYP/6-31G(d).²

For the reaction of enolborane with 2-methoxypropanal, the lowest energy transition state, 3, also has the methoxy group anti to the carbonyl (see Figure 2). However, the lowest energy transition state for the reaction of 2-methylthiopropanal, 4, has the MeS group perpendicular to the carbonyl, as predicted by the Felkin-Anh model. Similarly, the lowest energy transition states for the addition to 2-dimethylaminopropanal (5) and to 2-dimenthylphosphinopropanal (6) follow the Felkin-Anh model.

The lowest energy conformer of propanal with F, Cl, or OMe as the 2-substituent has the substituent anti to the carbonyl. All three of these aldehydes undergo addition of enolborane through the Cornforth TS. The lowest energy conformer with SMe₂ or PMe₂ has the substituent perpendicular to the carbonyl, which mimics its location in the enolborane transition state. Only 2-dimethylaminopropanal falls outside this pattern; its lowest energy conformer positions the substituent about 150° from the carbonyl, but rotation to a perpendiculat (Felkin-Anh) position requires only 2 kcal mol^-1, half of that need for F, Cl, or methoxy rotation. Cee, Cramer, and Evans draw two conclusions. First, the stereochemistry 1,2-addition of enolborane parallels the conformation of the aldehyde itself, and second, this implies that the Cornforth pathway can be preferred over the Felkin-Anh for those aldehydes where the anti conformation is particularly stable.

3 xyz file		4 xyz file
5 xyz file		6 xyz file

References

(1) Frenking, G.; F., K. K.; Reetz, M. T., “On the Origin of π-Facial Diastereoselectivity in Nucleophilic Additions to Chiral Carbonyl Compounds. 2. Calculated Transition State Structures for the Addition of Nucleophiles to Propionaldehyde 1, Chloroacetyldehyde 2, and 2-Chloropropionaldehyde 3.,” Tetrahedron 1991, 47, 9005-9018, DOI: 10.1016/S0040-4020(01)86505-4.

(2) Cee, V. J.; Cramer, C. J.; Evans, D. A., “Theoretical Investigation of Enolborane Addition to α-Heteroatom-Substituted Aldehydes. Relevance of the Cornforth and Polar Felkin-Anh Models for Asymmetric Induction,” J. Am. Chem. Soc. 2006, 128, 2920-2930, DOI: DOI: 10.1021/ja0555670

(3) Evans, D. A.; Siska, S. J.; Cee, V. J., “Resurrecting the Cornforth Model for Carbonyl Addition: Studies on the Origin of 1,2-Asymmetric Induction in Enolate Additions to Heteroatom-Substituted Aldehydes,” Angew. Chem. Int. Ed. 2003, 42, 1761-1765, DOI: 10.1002/anie.200350979.

A Stable Bis-allyl Intermediate on the Cope PES

As discussed in Chapter 3.2, the prototypical Cope rearrangement (the degenerate rearrangement of 1,5-hexadiene 1) is understood to proceed through a single concerted transition state. The concerted transition state 2 is described by three resonance structures (Scheme 1), and this allows for understanding the chameleonic nature of the substituted Cope rearrangement. For example, radical stabilizing groups at the 2 and 5 positions would favor the cyclohexyl-diyl structure.

Scheme 1

Schreiner computed the reaction path at BD(T)/cc-pVDZ//BLYP/6-31G* for 64 different variations of the Cope rearrangement.¹ A representative sampling from these is presented in Figure 1. The Cope rearrangements are found to fall into one of three categories. The first, called type 1, are concerted rearrangements. Type 2 rearrangements have two competing pathways: either through a concerted transition state or a diradical intermediate. The last group, type 3, comprises nonconcerted reactions with a cyclohexyl-diyl intermediate. Schreiner generalizes the results to the following rule: a nonconcerted reaction takes place when biradical intermediates are stabilized either by allyl or aromatic resonance.

Figure 1. Examples of the three type of Cope rearrangements. Relative energies, in kcal mol-1, were computed at BD(T)/cc-pVDZ//BLYP/6-31G*.1

Interestingly, Schreiner’s study identified reactions where the diyl is a stable intermediate, but he identified no case where the other extreme – two allyl radicals – appeared as a stable intermediate. Kertesz, in 2006, discovered just such an example with the Cope rearrangement of 3.² Using B3LYP and BPW91 computations with two different basis sets, he identified the stable diradical 5. This structure, shown in Figure 2, clearly has very long distances – 2.836 Å – separating the ends of the two “allylic” components. A true transition state 4 connects the reactant 3 with the intermediate 5 (see Figure 2). The activation energy is 6.3 kcal mol^-1 and the intermediate 5 lies 3.3 kcal mol^-1 above 3.

3	4	5
xyz file	xyz file	xyz file
Figure 2. B3LYP/6-31G(d) optimized structures of 3-5. Distances (Å) shown are between C1-C6 and C3-C4 of the hexadiene component of the Cope rearrangement.2

Why does a stable bis-allyl analogue exist on the Cope reaction surface of 3? In the prototype Diels-Alder reaction of 1,5-hexadiene, the possible bis-allyl intermediate (i.e., two isolated allyl radicals) is about 26 kcal mol^-1 higher in energy than the Cope transition state. Only with significant radical stabilization might one expect a bis-allyl intermediate to occur. One can consider 5 as composed of two bridged phenalenyl radicals (6). Phenalenyl radical is stable due to electron delocalization; its ESR spectrum has been observed, but it has not been isolated, instead dimerizing to give 7.³ In addition to the stabilization afforded by the extensive delocalization of the radical within the phenalenyl system, two phenalenyl systems can also interact through overlap of their π-systems, creating what has been termed π-dimerization.^4-6 MRMP2 computations suggest that the π-dimerization energy of 6 is 11 kcal mol^-1.⁷ While the geometry of 5 is not ideal for π-dimerization, its structure clearly indicates some stacking of the two phenalenyl fragments. Both the enhanced electron delocalization about the large phenalenyl system along with π-dimerization provides sufficient stabilization that the bis-allyl intermediate exits on the Cope rearrangement pathway. This now completes all of the options for how the Cope rearrangement may occur: either directly through a concerted transition state, or multi-step process with a 1,6-diyl intermediate or a bis-allyl intermediate.

Cope Rearrangement of 3-Vinylmethylenecyclobutane

3-Vinylmethylenecyclobutane 8 can undergo a myriad of thermal rearrangements involving [1,3]- and [3,3]-shifts.⁸ The Cope rearrangement of 8 to 9 has a barrier of 35.7 kcal mol^-1.⁹ This large barrier is consistent with cleavage of a C-C bond leading to a diradical intermediate.

Houk has recently confirmed the diradical nature of this rearrangement.¹⁰ The geometries of all reactants intermediates, products and transition states were optimized at UB3LYP/6-31+G(d) and single-point energies were evaluated at CASPT2(6,6)/6-31G(d). Two diradical intermediates, 10 and 11, lie 30.0 and 32.0 kcal mol^-1, respectively, above 8. These intermediates are separated by a small barrier, 1.5 kcal mol^-1 from 10, and a barrier of 2.0 kcal mol^-1 interconverts mirror versions of 10. All of these paths are sketched in Scheme 3 and the geometries of the critical points are displayed in Figure 3.

Scheme 3

8 xyz file
TS8-10 xyz file	TS8-11 xyz file
10 xyz file	TS10-11 xyz file	11 xyz file
TS11-9x xyz file	TS11-9n xyz file
9 xyz file

Figure 3. Optimized Structures of the critical points in Scheme 3.¹⁰

Only the reaction going forward from 11 can lead to product 9. There are two such routes, involving an exo or endo approach. They are of similar energy, and also very close in energy to that of the diradical intermediates. Houk concludes that the diradical intermediates “have substantial conformational freedom and very low barriers for forming stereo- and regioisomeric forms of the ring-enlarged product”, in agreement with the experimentally observed lack of any region- or stereoselectivity in the thermal reactions of 8. The computed barrier, 34.9 kcal mol^-1 for TS8-10, is in good accord with the experimental barrier of 35.7 kcal mol^-1.

A study by Jung¹¹ the year before actually inspired Houk’s work. Jung discovered that appropriately substituted vinylmethylcyclohexenes will undergo very selective Cope rearrangements; for example, thermolysis of 8a produces 9a in greater than 90% yield. This result is quite contrary to that normally observed for vinylmethylcyclohexene thermoylsis: many products with virtually complete scrambling of all stereochemical information.

Examination of the rearrangement of 8a is computationally prohibitive, so Houk looked at the effect of individual substituents. The role of the trialkylsiloxy group was evaluated through the rearrangement of 8b, leading to diradicals 10b and 11b (Scheme 4). The transition state leading to 11b is 1.5 kcal mol^-1 below that leading to 10b. This is opposite the relative ordering of the transition states in the parent reaction, indicating that siloxy substitution would favor the path that leads to direct Cope rearrangement, which must pass through 11. The preference for the opposite TS with the siloxy group results from its torquoselectivity (See Chapter 3.5) Since 11b is more stable than 10b, this would also help preserve the stereochemistry during the rearrangement.

Scheme 4

The effects of the terminal substituents were also evaluated. As shown in Scheme 5, the Cope rearrangement of 8b is predicted to proceed with distinct stereoselectivity. The ring opening step preferentially produces diradical intermediate 12 over 13. The ring forming step is also stereoselective: 12 cyclizes to 14 in a 3:1 ratio, while the ring closure of 13 predominantly gives 15. Overall, the rearrangement of 8b is predicted to give a product ratio 14:15 of 2:1. This is in accord with the Jung’s experimental observation.

Scheme 5

References

(1) Navarro-Vazquez, A.; Prall, M.; Schreiner, P. R., “Cope Reaction Families: To Be or Not to Be a Biradical,” Org. Lett. 2004, 6, 2981-2984, DOI: 10.1021/ol0488340

(2) Huang, J.; Kertesz, M., “Stepwise Cope Rearrangement of Cyclo-biphenalenyl via an Unusual Multicenter Covalent π-Bonded Intermediate,” J. Am. Chem. Soc. 2006, 128, 7277-7286, DOI: 10.1021/ja060427r

(3) Zheng, S.; Lan, J.; Khan, S. I.; Rubin, Y., “Synthesis, Characterization, and Coordination Chemistry of the 2-Azaphenalenyl Radical,” J. Am. Chem. Soc. 2003, 125, 5786-5791, DOI: 10.1021/ja029236o

(4) Goto, K.; Kubo, T.; Yamamoto, K.; Nakasuji, K.; Sato, K.; Shiomi, D.; Takui, T.; Kubota, M.; Kobayashi, T.; Yakusi, K.; Ouyang, J., “A Stable Neutral Hydrocarbon Radical: Synthesis, Crystal Structure, and Physical Properties of 2,5,8-Tri-tert-butyl-phenalenyl,” J. Am. Chem. Soc. 1999, 121, 1619-1620, DOI: 10.1021/ja9836242

(5) Suzuki, S.; Morita, Y.; Fukui, K.; Sato, K.; Shiomi, D.; Takui, T.; Nakasuji, K., “Aromaticity on the Pancake-Bonded Dimer of Neutral Phenalenyl Radical as Studied by MS and NMR Spectroscopies and NICS Analysis,” J. Am. Chem. Soc. 2006, 128, 2530-2531, DOI: 10.1021/ja058387z

(6) Takano, Y.; Taniguchi, T.; Isobe, H.; Kubo, T.; Morita, Y.; Yamamoto, K.; Nakasuji, K.; Takui, T.; Yamaguchi, K., “Hybrid Density Functional Theory Studies on the Magnetic Interactions and the Weak Covalent Bonding for the Phenalenyl Radical Dimeric Pair,” J. Am. Chem. Soc. 2002, 124, 11122-11130, DOI: 10.1021/ja0177197

(7) Small, D.; Zaitsev, V.; Jung, Y.; Rosokha, S. V.; Head-Gordon, M.; Kochi, J. K., “Intermolecular π-to-π Bonding between Stacked Aromatic Dyads. Experimental and Theoretical Binding Energies and Near-IR Optical Transitions for Phenalenyl Radical/Radical versus Radical/Cation Dimerizations,” J. Am. Chem. Soc. 2004, 126, 13850-13858, DOI: 10.1021/ja046770i

(8) Kozhushkov, S. I.; Kuznetsova, T. S.; Zefirov, N. S., “Mechanism of Thermal Isomerization of 3-Vinylmethylenecyclobutane into 4-Methylenecyclohexane,” Dokl. Akad. Nauk SSSR, 1988, 299, 1395-1399,

(9) Dolbier, W. R.; Mancini, G. J., “Non-concerted Thermal Reorganizations 3,3-Divinylmethylenecyclobutane,” Tetrahedron Lett. 1975, 16, 2141-2144, DOI: 10.1016/S0040-4039(00)72661-X.

(10) Zhao, Y. L.; Suhrada, C. P.; Jung, M. E.; Houk, K. N., “Theoretical Investigation of the Stereoselective Stepwise Cope Rearrangement of a 3-Vinylmethylenecyclobutane,” J. Am. Chem. Soc. 2006, 128, 11106-11113, DOI: 10.1021/ja060913e

(11) Jung, M. E.; Nishimura, N.; Novack, A. R., “Versatile Diastereoselectivity in Formal [3,3]-Sigmatropic Shifts of Substituted 1-Alkenyl-3-alkylidenecyclobutanols and Their Silyl Ethers,” J. Am. Chem. Soc. 2005, 127, 11206-11207, DOI: 10.1021/ja051663p

InChI

3: InChI=1/C34H26/c1-19-21-11-12-22-16-24-8-6-10-26-18-28-14-13-27-17-25-9-5-7-23(15-21)29(25)31(19)33(27,3)34(28,4)32(20(22)2)30(24)26/h5-18H,1-4H3/b12-11-/t33-,34+

5: InChI=1/C34H26/c1-19-23-11-12-25-17-29-9-6-10-30-18-26(22(4)32(21(25)3)34(29)30)14-13-24-16-28-8-5-7-27(15-23)33(28)31(19)20(24)2/h5-18H,1-4H3/b12-11-,14-13-

6: InChI=1/C13H9/c1-4-10-6-2-8-12-9-3-7-11(5-1)13(10)12/h1-9H

7: InChI=1/C26H18/c1-5-17-9-3-11-23-21(15-13-19(7-1)25(17)23)22-16-14-20-8-2-6-18-10-4-12-24(22)26(18)20/h1-16,21-22H

8: InChI=1/C7H10/c1-3-7-4-6(2)5-7/h3,7H,1-2,4-5H2

9: InChI=1/C7H10/c1-7-5-3-2-4-6-7/h2-3H,1,4-6H2