The novel cyclophanes 1 and 2 have now been synthesized.¹ An interesting question is whether the bent pyrenes portion of the two molecules remains aromatic. The bending angles is 93.8° in 1 and 95.8° in 2. This distortion is readily apparent in Figure 1, which presents their B3LYP/6-311G(d,p) optimized geometries. NICS computations were used to assess the aromaticity of the pyrene portion. The central rings of pyrene have NICS(0) = -4.4 ppm. The corresponding values in 1 and 2 are -4.5 ppm. The apical rings of pyrene have NICS(0)= -11.9 ppm, while the value is -11.1 ppm in 1 and -11.0 ppm in 2. These calculations indicate that the molecule retains much of the aromaticity of the parent pyrene despite the significant out-of-plane distortions.

Figure 1. B3LYP/6-311G(d,p) optimized geometries of 1 and 2.¹

1

2

References

(1) Zhang, B.; Manning, G. P.; Dobrowolski, M. A.; Cyranski, M. K.; Bodwell, G. J., "Nonplanar Aromatic Compounds. 9. Synthesis, Structure, and Aromaticity of 1:2,13:14-Dibenzo[2]paracyclo[2](2,7)-pyrenophane-1,13-diene," Org. Lett., 2008, 10, 273-276, DOI: 10.1021/ol702703b.

InChIs

1: InChI=1/C34H20/c1-3-7-31-27-17-23-13-15-25-19-28(20-26-16-14-24(18-27)33(23)34(25)26)32-8-4-2-6-30(32)22-11-9-21(10-12-22)29(31)5-1/h1-20H/b29-21-,30-22-,31-27-,32-28-
InChIKey=RYJKEGNHXVXOPX-LISLPQAZBN

2: InChI=1/C82H52/c1-9-25-53(26-10-1)71-73(55-29-13-3-14-30-55)77(59-37-21-7-22-38-59)81-67-49-63-45-47-65-51-68(52-66-48-46-64(50-67)69(63)70(65)66)82-78(60-39-23-8-24-40-60)74(56-31-15-4-16-32-56)72(54-27-11-2-12-28-54)76(58-35-19-6-20-36-58)80(82)62-43-41-61(42-44-62)79(81)75(71)57-33-17-5-18-34-57/h1-52H/b79-61-,80-62-,81-67-,82-68-
InChIKey=BKSFSTJXYFPKOG-IPILNRTDBN

I discuss computational prediction of optical rotation in Chapter 1.6.3. I want to address a new protocol for determining absolute configuration using computed spectral properties and a recent review of state-of-the-art computational methods for predicting optical activity.

Stephens and the Gaussian personnel developed the techniques for computing optical rotation, electronic circular dichroism (ECD) and vibrational circular dichroism (VCD).^1-4 Over the past year, Stephens has implemented a protocol for computing these properties in order to determine the absolute configuration of a chiral molecule.^5-7 The first application was to the structures of the related sesquiterpenes 1-4.⁵ A Monte Carlo conformational search is first carried out using MMFF94, and all low energy conformers are reoptimized at B3LYP/6-31G*. Restricted searches by varying some dihedral angles are also sometimes used to insure that all reasonable low-energy conformations have been identified. Then, using these optimized geometries,specific rotations and ECD are computed at TDDFT/B3LYP/aug-cc-pVDZ, and IR and VCCD spectra computed at B3LYP and B3PW91 with the TZ2P basis set.

The computed and experimental optical rotations at the sodium D line for 1-4 are listed in Table 1. The computed values of [α]_D for 1 as the 1R,2R,5S,8R,11R isomer (as shown above) is in reasonable agreement with the experimental value – with error similar to those I describe in the book. This is in agreement with the assigned absolute configuration of naturally occurring 1. While the core structures of 2-4 are likely to be identical to 1 assuming similar biosynthesis, their absolute configurations have not been determined. The computed optical rotation for 3 and 4 are again in reasonable agreement with experiment, but for 2 the errors are large for either enantiomer. This is where ECD and VCD are valuable. The computed ECD and VCD spectra of 1 are in extraordinary agreement with the experimental spectra, confirming the assigned absolute configuration. Stephens reports the ECD and VCD spectra of 2-4 and finds that they all have identical configurationas of the core. He suggests that experimental determination of these VCD spectra will confirm all of their absolute configurations.

Table 1. Experimental and computed optical rotation for 1-4 at the sodium D line.

^aRef. 8. ^bRef. 9. ^cRef. 10. ^eRef. 5. ^eRef. 11

A second study involved the iridoids 5 and 6.⁷ Plumericin 5 has the absolute configuration shown below with [α]_D = +204. The more recently discovered prismatomerin 6 has [α]_D = -136, suggesting that the core polycyclic portion may have opposite absolute configuration. Stephens prepared the acetate of 6 and experimentally determined its VCD spectrum. The VCD spectrum was then computed using the above protocol. The computed spectrum for the enantiomer with the same absolute configuration as 5 matches the experimental spectrum. Thus, 5 and 6 have the same absolute configuration. Stephens concludes with the warning that optical activity of analogous compounds can be quite different and is not suitable for obtaining configuration information. Rather, VCD is a much more suitable test, especially when experimental and computed spectra are utilized.

I will finish this post with a brief recap of the optical rotation computations a few of the molecules discussed in a recent review by Crawford.¹² Crawford implements a linear-response coupled clusters with modified velocity gauge protocol. He compares the optical rotation computed with this method, the time-dependent DFT approach developed by Stephens et al and experiment. He describes systems where the CC approach performs much better than DFT, where DFT performs better than CC, but for the wrong reason, and a case where DFT appears to perform better than CC.

The optical rotation of (P)-(+)-[4]-triangulane 7 at a variety of wavelengths has been determined both experimentally and computationally. These results are listed in Table 2. It is readily apparent that CCSD performs much better than DFT. The poor performance of the DFT method is linked to electronic excitation energies that are too small.

Table 2. Optical rotation of 7.

^aRef. 13. ^bRef. 14.

The ORD of (S)-methyloxirane show a change of sign: -8.39 at 633 nm and +7.39 at 355 nm. CCSD predicts a reasonable value at 633 nm but gets the wrong sign at the shorter wavelength. On the other hand, B3LYP does predict the sign change. However, this seemingly correct result is due to (once again) underestimation of the excitation energy.

Lastly, Crawford reports on his study of (1S,4S)-norbornenone. The optical rotation of the sodium D line is -1146, and B3LYP does a very reasonable job in predicting a value of -1214. However, CCSD(MVG) grossly underestimates this value at -558. Though B3LYP again underestimates the excitation energy it appears to get the energy and rotational strength near the liquid-phase values. Most worrisome is that Crawford discounts basis set improvements and higher order correlation effects, and holds some hope for a significant difference in gas-phase vs solution phase rotations.

References

(1) Stephens, P. J., "Theory of Vibrational Circular Dichroism," J. Phys. Chem. 1985, 89, 748-752, DOI: 10.1021/j100251a006.

(2) Cheeseman, J. R.; Frisch, M. J.; Devlin, F. J.; Stephens, P. J., "Hartree-Fock
and Density Functional Theory ab Initio Calculation of Optical Rotation Using GIAOs: Basis Set
Dependence," J. Phys. Chem. A, 2000, 104, 1039-1046, DOI: 10.1021/jp993424s.

(3) Stephens, P. J.; Devlin, F. J.; Cheeseman,J. R.; Frisch, M. J., "Calculation of Optical Rotation Using Density Functional Theory," J. Phys. Chem. A, 2001, 105, 5356-5371, DOI: 10.1021/jp0105138.

(4) Stephens, P. J.; McCann, D. M.; Cheeseman, J. R.; Frisch, M. J., "Determination of absolute configurations of chiral molecules using ab initio time-dependent Density Functional Theory calculations of optical rotation: How reliable are absolute configurations obtained for molecules with small rotations?," Chirality, 2005, 17, S52-S64, DOI: 10.1002/chir.20109.

(5) Stephens, P. J.; McCann, D. M.; Devlin, F. J.; Smith, A. B., "Determination of the Absolute Configurations of Natural Products via Density Functional Theory Calculations of Optical Rotation, Electronic Circular Dichroism, and Vibrational Circular Dichroism: The Cytotoxic Sesquiterpene Natural Products Quadrone, Suberosenone, Suberosanone, and Suberosenol A Acetate," J. Nat. Prod., 2006, 69, 1055-1064, DOI: 10.1021/np060112p.

(6) Stephens, P. J.; Pan, J. J.; Devlin, F. J.; Urbanova, M.; Hajicek, J., "Determination of the Absolute Configurations of Natural Products via Density Functional Theory Calculations of Vibrational Circular Dichroism, Electronic Circular Dichroism and Optical Rotation: The Schizozygane Alkaloid Schizozygine," J. Org. Chem., 2007, 72, 2508-2524, DOI: http://dx.doi.org/10.1021/jo062567p.

(7) Stephens, P. J.; Pan, J. J.; Krohn, K., "Determination of the Absolute Configurations of Pharmacological Natural Products via Density Functional Theory Calculations of Vibrational
Circular Dichroism: The New Cytotoxic Iridoid Prismatomerin," J. Org. Chem., 2007, 72, 7641-7649, DOI: 10.1021/jo071183b.

(8) Smith, A. B.; Konopelski, J. P.; Wexler, B. A.; Sprengeler, P. A., "Quadrone structural and synthetic studies. Total synthesis of natural (-)-quadrone, the (+)-enantiomer, and the racemate. Conformational analysis, circular dichroism, and determination of absolute stereochemistry," J. Am. Chem. Soc., 1991, 113, 3533-3542, DOI: 10.1021/ja00009a047.

(9) Wijeratne, E. M. K.; Turbyville, T. J.; Zhang, Z.; Bigelow, D.; Pierson, L. S.; VanEtten, H. D.; Whitesell, L.; Canfield, L. M.; Gunatilaka, A. A. L., "Cytotoxic Constituents of Aspergillus terreus from the Rhizosphere of Opuntia versicolor of the Sonoran Desert," J. Nat. Prod., 2003, 66, 1567-1573, DOI: 10.1021/np030266u.

(10) Bokesch, H. R.; McKee, T. C.; Cardellina II, J. H.; Boyd, M. R., "Suberosenone, a new cytotoxin from Subergorgia suberosa," Tetrahedron Lett., 1996, 37, 3259-3262, DOI: 10.1016/0040-4039(96)00528-X

(11) Sheu, J. H.; Hung, K. C.; Wang, G. H.; Duh, C. Y., "New Cytotoxic Sesquiterpenes from the Gorgonian Isis hippuris," J. Nat. Prod., 2000, 63, 1603-1607, DOI: 10.1021/np000271n.

(12) Crawford, T. D.; Tam, M. C.; Abrams, M. L., "The Current State of Ab Initio Calculations of Optical Rotation and Electronic Circular Dichroism Spectra," J. Phys. Chem. A, 2007, 111, 12057-12068, DOI: 10.1021/jp075046u.

(13) Crawford, T. D.; Owens, L. S.; Tam, M. C.; Schreiner, P. R.; Koch, H., "Ab Initio Calculation of Optical Rotation in (P&)-(+)-[4]Triangulane," J. Am. Chem. Soc., 2005, 127, 1368-1369, DOI: 10.1021/ja042787p.

(14) de Meijere, A.; Khlebnikov, A. F.; Kozhushkov, S. I.; Kostikov, R. R.; Schreiner, P. R.; Wittkopp, A.; Rinderspacher, C.; Menzel, H.; Yufit, D. S.; Howard, J. A. K., "The First Enantiomerically Pure [n]Triangulanes and Analogues: σ-[n]Helicenes with Remarkable Features," Chem. Eur. J., 2002, 8, 828-842, DOI: 10.1002/1521-3765(20020215)8:4<828::AID-CHEM828>3.0.CO;2-Y

InChIs

1: InChI=1/C15H20O3/c1-14(2)7-15-9-4-3-8(14)10(15)5-12(16)11(15)6-18-13(9)17/h8-11H,3-7H2,1-2H3/t8?,9-,10?,11?,15?/m1/s1 PubChem
        InChIKey: BBIDMUQZCCGABN-UDZYVRSQBU

2: InChI=1/C15H22O/c1-9-5-6-11-12-7-13(16)10(2)15(9,12)8-14(11,3)4/h9,11-12H,2,5-8H2,1,3-4H3/t9-,11?,12?,15?/m0/s1
        InChIKey: JDGYVUJBJYXKSX-NCLPGTSEBA

3: InChI=1/C15H24O/c1-9-5-6-11-12-7-13(16)10(2)15(9,12)8-14(11,3)4/h9-12H,5-8H2,1-4H3/t9-,10+,11?,12?,15?/m0/s1
      InChIKey: KHINYKJYBNWSSP-BIGXPMCQBN

4: InChI=1/C17H26O2/c1-10-6-7-13-14-8-15(19-12(3)18)11(2)17(10,14)9-16(13,4)5/h10,13-15H,2,6-9H2,1,3-5H3/t10-,13?,14?,15+,17?/m0/s1
      InChIKey: UZRAQUNNGNYEHD-XDUGHSHMBF

5: InChI=1/C16H18O5/c1-3-8-11-6-12-13-9(10(7-20-12)14(17)19-2)4-5-16(11,13)21-15(8)18/h3,7,9,11-13H,4-6H2,1-2H3/b8-3+/t9-,11-,12-,13-,16-/m1/s1
      InChIKey: QOWSZGWHIKPQIA-WCDIAXTGBA
PubChem

6: InChI=1/C21H20O6/c1-25-19(23)15-10-26-17-9-16-14(8-11-2-4-12(22)5-3-11)20(24)27-21(16)7-6-13(15)18(17)21/h2-5,8,10,13,16-18,22H,6-7,9H2,1H3/b14-8+/t13-,16-,17-,18-,21-/m1/s1
      InChIKey: OXYVEVVOLQYXPZ-SOSYHPOKBY

7: InChI=1/C9H12/c1-2-7(1)5-9(7)6-8(9)3-4-8/h1-6H2
      InChIKey: JCHCWAJGYWGXMQ-UHFFFAOYAV

I guess one can never know enough about the S_N2 reaction! Wester and co-workers have performed careful crossed molecular beam imagining on the reaction Cl^– + CH₃I.¹ In collaboration with Hase, they have employed MP2/ECP/aug-cc-pVDZ computations to get the potential energy surface for the reaction and direct molecular dynamics. The PES is exactly as one would expect for a gas phase ion-molecule reaction: the transition state has backside attack of the nucleophile and it connects to two ion-dipole complexes (see Chapter 5.1.1).

The experiments are interpreted with the help of the MD computations. At low energy one sees formation of the complex. At higher energies, the direct backside attack reaction occurs. And at higher energies a new reaction path emerges, as sketched out in Figure 1. As the nucleophile (chloride) approaches methyl iodide, the methyl group rotates towards the nucleophile. The methyl group then collides with the nucleophile, which sends the methyl group spinning about the iodine atom in the opposite direction. The methyl group rotates all the way around the iodine atom and when it approaches the chloride a second time, the displacement reaction occurs and product is formed. They term this process a “roundabout mechanism”, and they have some experimental evidence for the occurrence of the double roundabout (two rotations of the methyl group about the iodine)! I think we should anticipate seeing more and more interesting reaction pathways as experimental and theoretical techniques continue to allow us a more detailed and precise view of motion of individual molecules across barriers.

Figure 1. Schematic of the trajectory illustrating the roundabout mechanism.
Chlorine is yellow, iodine is pink and carbon is black.

References

(1) Mikosch, J.; Trippel, S.; Eichhorn, C.; Otto, R.; Lourderaj, U.; Zhang, J. X.; Hase, W. L.; Weidemüller, M.; Wester, R., "Imaging Nucleophilic Substitution Dynamics," Science 2008, 319, 183-186, DOI: 10.1126/science.1150238.

The bond dissociation energies (BDE) of the O-H bond of oximes R₁R₂C=N-OH) are discussed in Chapter 2.1.1.2. The controversy associated with these values originates from conflicting experimental data coming from calorimetric and electrochemical experiments. Some of the conflicting data are listed in Table 1. The electrochemical method provides energies at least a couple of kcal mol^-1 too large, sometimes much more than that. I described in the book some composite method computations (G3MP, G3, CBS-QB3 and CBS-ANO)¹ that suggest the BDE of acetone oxime is around 85 kcal mol^-1, consistent with the calorimetric results. These authors could not apply these expensive methods to other compounds and were forced to use UB3LYP, which underestimates the values of the BDEs.

Table 1. BDEs (kcal mol^-1) from calorimetric and electrochemical experiments
and ONIOM-G3B3 computations.

^aRef. 2. ^bRef. 3. ^cRef. 1. ^dRef. 4. ^eRef. 5

Fu⁶ has now applied the ONIOM-G3B3⁷ approach to this problem. This is a clever way of attacking large molecules that require rather large computations to appropriately treat the quantum mechanics. So, each step of the G3B3 composite method is split into two levels: the high level is computed with the appropriate method from the G3B3 procedure, while the low level is treated with B3LYP. These resulting BDEs are listed in Table 1 and show remarkably nice agreement with the calorimetric results. These computed BDEs confirm that the electrochemical results are in error. Fu also computed the BDEs of some 30 other oximes for which electrochemical BDEs are available and for the large majority of these compounds, the electrochemical values are again too large.

References

(1) Pratt, D. A.; Blake, J. A.; Mulder, P.; Walton, J. C.; Korth, H.-G.; Ingold, K. U., "O-H Bond Dissociation Enthalpies in Oximes: Order Restored," J. Am. Chem. Soc. 2004, 126, 10667-10675, DOI: 10.1021/ja047566y.

(2) Mahoney, L. R.; Mendenhall, G. D.; Ingold, K. U., "Calorimetric and Equilibrium Studies on Some Stable Nitroxide and Iminoxy Radicals. Approximate Oxygen-Hydrogen Bond Dissociation Energies in Hydroxylamines and Oximes," J. Am. Chem. Soc. 1973, 95, 8610-8614, DOI: 10.1021/ja00807a018.

(3) Bordwell, F. G.; Ji, G.-Z., "Equilibrium Acidities and Homolytic Bond Dissociation Energies of the H-O Bonds in Oximes and Amidoximes," J. Org. Chem. 1992, 57, 3019 – 3025, DOI: 10.1021/jo00037a014.

(4) Bordwell, F. G.; Zhang, S., "Structural Effects on Stabilities of Iminoxy Radicals," J. Am. Chem. Soc. 1995, 117, 4858-4861, DOI: 10.1021/ja00122a016.

(5) Bordwell, F. G.; Liu, W.-Z., "Solvent Effects on Homolytic Bond Dissociation Energies of Hydroxylic Acids," J. Am. Chem. Soc. 1996, 118, 10819-10823, DOI: 10.1021/ja961469q.

(6) Chong, S. S.; Fu, Y.; Liu, L.; Guo, Q. X., "O-H Bond Dissociation Enthalpies of Oximes: A Theoretical Assessment and Experimental Implications," J. Phys. Chem. A 2007, 111, 13112-13125, DOI: 10.1021/jp075699a.

(7) Li, M. J.; Liu, L.; Fu, Y.; Guo, Q. X., "Development of an ONIOM-G3B3 Method to Accurately Predict C-H and N-H Bond Dissociation Enthalpies of Ribonucleosides and Deoxyribonucleosides," J. Phys. Chem. B 2005, 109, 13818-13826, DOI: 10.1021/jp0508204.

What happens when antiaromatic rings stack? One can draw an MO interaction diagram for π-stacked cyclobutadiene dimer (Figure 1) and recognize at once that this cluster should be stabilized. In fact, it is reminiscent of an orbital diagram for an aromatic species!

Figure 1. MO Interaction diagram of stacked butadiene (modified from Ref 1).

Houk had examined just this dimer (1) in 1996 and located a D_4h critical point at CASSCF(8,8)/6-31G* (see Figure 2).² This structure is energetically below two isolated cyclobutadiene molecules; however, it is a second-order saddle point.

1

Figure 1. CASSCF(8,8)/6-31G* optimized structure of 1.

Schleyer has examined a series of superphanes constructed from anti- and aromatic rings linked by methano bridges, 2-7.¹ These structures were optimized at B3LYP/6-311+G** and their magnetic properties computed at GIAO-PW91. The optimized structures of 3 and 4 are shown in Figure 3.

3

4

Figure 3. B3LYP/6-311+G** optimized structures of 3 and 4.¹

The inter-ring separation (D) in these compounds is quite interesting (Table 1). It decreases in the series 2-4, with the distance in the latter compound of only 2.002 Å. The inter-ring distance is much larger in 5, which has two (aromatic) benzene rings. All of the other comounds (except 2) have shorter distances and these all involve antiaromatic rings. These short distances for the antiaromatic superphanes suggests stabilizing interactions between the rings, as indicated by the MO diagram of Figure 1.

Table 1. Inter-ring distance and NICS values for 2-7.¹

^aDistance (Å) between the carbon of one ring and the closest carbon of the second ring.

The NICS values are also interesting. Schleyer computed a variety of different NICS values, and we list here the isotropic NICS value at the cage center (NICS_cage) and the zz-component evaluated 1 Å above the ring on the outside face NICS(1)_zzring). The NICS(1)_zzring is perhaps the best measure of magnetic properties related to aromatic/antiaromatic character. All six compounds have rings that have negative values of NICS(1)_zzring, indicating of aromatic character. In fact, the value for 5 is less negative than for isolated benzene alone. This suggests that the stacked antiaromatic rings become aromatic, while the stacked aromatic rings become less aromatic. For all six compounds, the NICS_cage value is negative indicating diatropicity, associated with aromatic character – again consistent with the MO argument presented in Figure 1. To answer our lead off question, stacked antiaromatic rings are aromatic!

References

(1) Corminboeuf, C.; Schleyer, P. v. R.; Warner, P., "Are Antiaromatic Rings Stacked Face-to-Face Aromatic?," Org. Lett. 2007, 9, 3263-3266, DOI: 10.1021/ol071183y.

(2) Li, Y.; Houk, K. N., "The Dimerization of Cyclobutadiene. An ab Initio CASSCF Theoretical Study," J. Am. Chem. Soc. 1996, 118, 880-885, DOI: 10.1021/ja921663m.

InChIs

2: InChI=1/C9H6/c1-4-6-2-7-5(1)9(7)3-8(4)6/h1-3H2/q-2

3: InChI=1/C12H8/c1-5-7-2-8-6(1)10-3-9(5)11(7)4-12(8)10/h1-4H2

4: InChI=1/C15H10/c1-6-8-2-9-7(1)11-3-10(6)14-5-15(11)13(9)4-12(8)14/h1-5H2/q+2

5: InChI=1/C18H12/c1-7-9-2-10-8(1)12-3-11(7)15-5-16(12)18-6-17(15)13(9)4-14(10)18/h1-6H2

6: InChI=1/C21H14/c1-8-10-2-11-9(1)13-3-12(8)16-5-17(13)21-7-20(16)18-6-19(21)15(11)4-14(10)18/h1-7H2/q-2

7: InChI=1/C24H16/c1-9-11-2-12-10(1)14-3-13(9)17-5-18(14)22-7-21(17)23-8-24(22)20-6-19(23)15(11)4-16(12)20/h1-8H2

In Chapter 5.3.2, I extensively discuss the organocatalyzed aldol reaction. Barbas and List have pioneered the use of proline to catalyze this reaction, and Houk has performed a series of computational studies to discern the mechanism. The mechanism is essentially the attack of the enamine on the carbonyl with concomitant proton transfer from the carboxylic acid to the forming oxyanion.

Shininisha and Sunoj have examined a number of bicyclic analogues of proline (1-11) as catalysts of the aldol reaction.¹ They computed the activation energies for the reaction of the enamine derived from acetone with p-nitrobenzaldehyde with the various catalysts. All computations were performed at B3LYP/6-311+G**//B3LYP/6-31G* with the solvent effects modeled using CPCM.

As Houk has demonstrated, there are four possible transition states: the attack can come to either the re or si face of the aldehyde and either the syn or anti enamine can be the reactant. The four transition states for the reaction of 8 are shown in Figure 1. These TSs are representative of all of the transition states involving the different catalysts, including proline itself. These TS are characterized by proton transfer accompanying the C-C bond formation. Their relative energies can be interpreted in terms of the distortions about the enamine double bond (the more planar, the lower the energy) and the arrangement of the carboxylic acid and the incipient oxyanion. These arguments were made by Houk and are described in my book.

8-anti-re 0.0	8-anti-si 2.12
8-syn-re 8.15	8-syn-si 7.28

Figure 1. B3LYP/6-311+G**//B3LYP/6-31G* optimized structures and relative energies (kcal/mol) of the transition states of the enamine derived from acetone and 8 with p-nitrobenzaldehyde¹

The enantiomeric excess predicted by the computations for the aldol reaction using the 11 different bicyclic catalysts is presented in Table 1. All of the catalysts except 11 give high enantiomeric excess, with a number of them predicted to produce an ee above 90%. The authors conclude that these catalysts are worth exploring, since they are predicted to perform better than proline (which has a predicted ee of 75%).

Table 1. Predicted ee for the reaction of the enamine derived
from acetone and catalyst with p-nitrobenzaldehyde.

References

(1) Shinisha, C. B.; Sunoj, R. B., "Bicyclic Proline Analogues as Organocatalysts for Stereoselective Aldol Reactions: an in silico DFT Study," Org. Biomol. Chem., 2007, 5, 1287-1294, DOI: 10.1039/b701688c.

InChIs

1: InChI=1/C8H13NO2/c1-5-4-6-2-3-8(5,9-6)7(10)11/h5-6,9H,2-4H2,1H3,(H,10,11)

2: InChI=1/C8H13NO2/c1-5-4-8(7(10)11)3-2-6(5)9-8/h5-6,9H,2-4H2,1H3,(H,10,11)

3: InChI=1/C6H9NO2/c8-5(9)6-2-1-4(3-6)7-6/h4,7H,1-3H2,(H,8,9)

4: InChI=1/C6H9NO3/c8-5(9)6-2-1-4(7-6)10-3-6/h4

5: InChI=1/C5H7NO3/c7-4(8)5-1-3(6-5)9-2-5/h3,6H,1-2H2,(H,7,8)

6: InChI=1/C6H9NO2S/c8-5(9)6-2-1-4(7-6)10-3-6/h4,7H,1-3H2,(H,8,9)

7: InChI=1/C5H7NO2S/c7-4(8)5-1-3(6-5)9-2-5/h3,6H,1-2H2,(H,7,8)

8: InChI=1/C7H11NO2/c9-6(10)7-2-1-5(3-7)4-8-7/h5,8H,1-4H2,(H,9,10)

9: InChI=1/C7H11NO2/c9-7(10)6-4-1-2-5(3-4)8-6/h4-6,8H,1-3H2,(H,9,10)

10: InChI=1/C6H9NO2/c8-6(9)5-3-1-4(2-3)7-5/h3-5,7H,1-2H2,(H,8,9)

11: InChI=1/C6H9NO2/c8-6(9)5-3-1-4(5)7-2-3/h3-5,7H,1-2H2,(H,8,9)

The norbornyl cation has been a source of controversy for decades. Just what is the nature of this cation? Should one consider it a classical cation A or of some non-classical character B? A recent computational study adds further fuel to this fire.¹

The B3LYP/6-311G(d,p) structure of the norbornyl cation is shown in Figure 1, and this structure is little changed when reoptimized at PBE1PBE/6-311G(d,p) or CCSD/6-311G(d,p). Application of the topological method (sometimes referred to as atoms-in-molecules or AIM) reveals a bond path network that resembles the bicyclo[3.2.0]heptyl cation C. The C₁-C₂ distance is 1.75 Å and a bond path does connect these two atoms, though the density at the bond critical point is only 60% the value at the other C-C bonds in the compound. There is no bond path connecting C₁ to C₃ that would close up a three-member ring. The C₁-C₃ distance is 1.955 Å. So, the non-classical structure is not a proper description of this unusual species.

Figure 1. B3LYP/6-311G(d,p) optimized structure of the norbornyl cation.

References

(1) Werstiuk, N. H., "7-Norbornyl Cation – Fact or Fiction? A QTAIM-DI-VISAB Computational Study," J. Chem. Theory Comput., 2007, 3, 2258-2267, DOI: 10.1021/ct700176d.

In the book I extensively discuss the singlet-triplet gap of methylene and some of the chemistry of phenylcarbene. Schleyer and Schaefer have now reported computations on the singlet-triplet gap of arylcarbenes.¹ The geometries of phenylcarbene 1, diphenylcarbene 2, 1-naphthylcarbene 3, bis(1-naphtyl)carbene 4, and 9-anthrylcarbene 5 were optimized at B3LYP/6-311+G(d,p). These geometries are shown in Figure 1.

1s	1t
2s	2t
3s	3t
4s	4s
4s	4s

Figure 1. B3LYP/6-311+G(d,p) optimized structures of singlet and triplet 1-5.

Since this functional is known to underestimate the singlet-triplet gap of carbenes, they employ an empirical correction based on the difference in this gap for methylene between the computed value (11.89 kcal mol^-1) and the experimental value (9.05 kcal mol^-1). These corrected energy gaps are listed in Table 1.

Table 1. Corrected singlet-triplet energy gaps (kcal mol^-1) at B3LYP/6-311+G(d,p).

Using the following isodesmic reactions, they estimate the stabilization of the singlet or triplet carbene afforded by the aryl substituent:

R-C-H + CH₄ → H-C-H + R-CH₃

R-C-R + CH₄ → R-C-H + R-CH₃

These isodesmic energies are listed in Table 2. For phenylcarbne, the phenyl group stabilizes the singlet more than the triple, reducing the ST gap by 6.3 kcal mol^-1. However, adding a second phenyl group (making 2) stabilizes both the singlet and triplet by about the same amount, leading to little change in the ST gap. The singlet does not get accrue the potential benefit of the second aryl group because sterics prohibit the two rings from being coplanar.

Table 2. Aryl effect for 1-5 based on the isodesmic reaction energies (kcal mol^-1)

References

(1) Woodcock, H. L.; Moran, D.; Brooks, B. R.; Schleyer, P. v. R.; Schaefer, H. F., "Carbene Stabilization by Aryl Substituents. Is Bigger Better?," J. Am. Chem. Soc., 2007, 129, 3763-3770, DOI: 10.1021/ja068899t.

InChIs

1: InChI=1/C7H6/c1-7-5-3-2-4-6-7/h1-6H

2: InChI=1/C13H10/c1-3-7-12(8-4-1)11-13-9-5-2-6-10-13/h1-10H

3: InChI=1/C11H8/c1-9-5-4-7-10-6-2-3-8-11(9)10/h1-8H

4: InChI=1/C21H14/c1-2-8-19-14-16(12-13-17(19)6-1)15-20-10-5-9-18-7-3-4-11-21(18)20/h1-14H

5: InChI=1/C15H10/c1-11-14-8-4-2-6-12(14)10-13-7-3-5-9-15(11)13/h1-10H

Robinson and Schleyer report the synthesis of and computations on the novel structure gallepin 1.¹ This is the gallium analogue of tropyllium, the prototype of a seven-member aromatic ring. Robinson actually prepared the bis-benzannulated analogue 2, which is found to coordinate to TMEDA in the crystal.

Schleyer computed (B3LYP/LANL2DZ) the gallepin portion of 2 in its naked form 3 and associated with trimethylamine 4. The crystal structure of 2 reveals that the 7 member ring is boat-shaped, and this is reproduced in the computed structure of 4. Interestingly, the naked gallepin is planar, suggestive of an aromatic structure. NICS_πZZ computations were performed to gauge the aromaticity of these compounds. The value for the 7-member ring is -9.0 in 4 and -9.9 in 3, indicating aromatic character. These values are less then in the parent gallepin 1, which has a value of -15.3, but this is the normal type of diminishment expected from benzannulation.
But borapin has a NICS_πZZ substantially more negative (-27.7) and so gallepins are less aromatic than borapins. Nonetheless, it is very interesting that aromaticity can be extended in this interesting way – different heteroatom and different ring size.

3	4

References

(1) Quillian, B.; Wang, Y.; Wei, P.; Wannere, C. S.; Schleyer, P. v. R.; Robinson, G. H., "Gallepins. Neutral Gallium Analogues of the Tropylium Ion: Synthesis, Structure, and Aromaticity," J. Am. Chem. Soc., 2007, 129, 13380-13381, DOI: 10.1021/ja075428d.

In Chapter 7.3.5.1 I discuss the computational and experimental results of Singleton¹ regarding C₂-C₆ enyne allene cyclization. The reaction is shown below, and though Singleton could locate no transition state that connects the reactant to the diradical, molecular dynamics trajectory calculations show that the diradical is sampled, though the dominant pathway is the concerted route.

Schmittel has expanded on this work by determining the kinetic isotope effects for four more analogues.2 The results are summarized in Table 1. Depending on the substituent, the predominant pathway can be concerted or stepwise or even a mixture of these two (termed “boundary”). Schmittel argues that the region about the single transition state, the one that directly connect reactant to product through a concerted path, is actually quite flat. This is a “broad transition state zone”. Trajectories can traverse through various regions of the zone, some that go on to diradical, some that go on to product. Substituents can alter the shape of the TS zone and thereby shift the set of trajectories in one direction or the other. The upshot is further support for the importance on non-statistical dynamics in dictating the course of reactions.

Table 1. Kinetic isotope effects for C₂-C₆ enyne allene cyclizations

References

(1) Bekele, T.; Christian, C. F.; Lipton, M. A.; Singleton, D. A., ""Concerted" Transition State, Stepwise Mechanism. Dynamics Effects in C²-C⁶ Enyne Allene Cyclizations," J. Am. Chem. Soc. 2005, 127, 9216-9223, DOI: 10.1021/ja0508673.

(2) Schmittel, M.; Vavilala, C.; Jaquet, R., "Elucidation of Nonstatistical Dynamic Effects
in the Cyclization of Enyne Allenes by Means of Kinetic Isotope Effects," Angew. Chem. Int. Ed. 2007, 46, 6911-6914, DOI: 10.1002/anie.200700709