The structure of the simple, fundamental ethyl cation has finally been ascertained. Computational studies had long suggested the non-classical structure 1 for this cation. The classical structure 2 is a transition state for scrambling the protons. The MP2/6-311G(2d,p) geometries of both structures are shown in Figure 1.

1	2
1.Ar(C2v)	1.Ar(Cs)

Figure 1. MP2/6-311G(2d,f) structures of 1, 2, 1^.Ar(C_2v) and 1^.Ar(C_s).

Dopfer¹ has now obtained IR spectrum of ethyl cation by single-photon IR photodissociation spectroscopy through the reaction

C₂H₅^{+ .} Ar + hν → C₂H₅⁺ + Ar

Two structures of the ethyl cation associated with Ar were optimized at MP2/6-311G(2df,2pd). (The MP2/6-311G(2d,p) structures are shown in Figure 1.) Both of their computed IR spectra have stretches at nearly identical wavenumbers as for ethyl cation 1 itself. The experimental IR spectra has absorptions at 3317 and 3037 cm^-1, very close to the computed frequencies for 1^.Ar(C_2v). This provides strong experimental evidence that ethyl cation is in fact a non-classical ion.

References

(1) Andrei, H.-S.; Solcà, N.; Dopfer, O., "IR Spectrum of the Ethyl Cation: Evidence for the Nonclassical Structure," Angew. Chem. Int. Ed. 2008, 47, 395-397, DOI: 10.1002/anie.200704163

I have discussed Möbius aromatic systems in the book and in the blog. A new Möbius aromatic platform has been synthesized, where the porphyrin π-system is appropriately twisted. Osuka has prepared the hexaphyrins 1 and 2.¹ These possess a double-twist structure, and with its 28 π-electrons 1 should be antiaromatic and 2, having 26 π-electrons should be aromatic.

1

2

3

In fact, the x-ray structure of 1 displays significant bond alternation and the NH protons (in the interior of the molecule) have chemical shift far downfield (δ 14.95 and 12.35 ppm) – all consistent with antiaromatic character. On the other hand¸ while 2 exhibits little bond alternation, the NH protons are seen at 11.1 ppm, too far downfield for the interior positions of an aromatic compound!

Rzepa² has computed 1 and 2 at MPW1PW91/6-31G(d,p) for X=H and CF₃; the latter matches the experimentally prepared compounds. (Rzepa supplies very nice web-enabled access to his results through the supporting materials, and so I do not repeat his structures here. Please also see comments to this post.) As expected, both optimized structures of 1(X=H or X=CF₃) shows distinct bond localization and positive NICS values. The chemical shifts of the NH protons are far downfield, and in reasonable agreement with the experimental shifts. The optimized structures of 2 display bond delocalization and negative NICS values, indicative of aromaticity, as do the NH chemical shifts of 5.2 ppm (X=CF₃) or 3.8 ppm (X=H). These chemical shifts differ from the experiment. Rzepa locates a second less stable conformation 3, but its NH chemical shifts are at 10.9 and 10.1 ppm, in reasonable agreement with experiment. So, he concludes that 1 is antiaromatic and 2 is aromatic and both have a double-twist Möbius topology.

Tanaka, et al have reported the structure of the octaphyrin held in place by a complexed
metal, such as 4.³ A number of analogues have been prepared and their x-ray structure shows the single twist needed for Möbius topology. The NMR spectra are consistent with an aromatic system. And relevant to this blog, B3LYP/6-31G(d) (SDD for the heavy metals) NICS computations reveals a large negative value, -14.6 ppm for 5.

4: R = perfluorophenyl 5: R = H

References

(1) Shimizu, S.; Aratani, N.; Osuka, A., "meso-Trifluoromethyl-Substituted
Expanded Porphyrins," Chem. Eur. J., 2006, 12, 4909-4918, DOI: 10.1002/chem.200600158

(2) Rzepa, H. S., "Lemniscular Hexaphyrins as Examples of Aromatic and Antiaromatic
Double-Twist Möbius Molecules," Org. Lett. 2008, DOI: 10.1021/ol703129z

(3) Tanaka, Y.; Saito, S.; Mori, S.; Aratani, N.; Shinokubo, H.; Shibata, N.; Higuchi, Y.; Yoon, Z. S.; Kim, K. S.; Noh, S. B.; Park , J. K.; Kim , D.; Osuka, A., "Metalation of Expanded Porphyrins: A Chemical Trigger Used To Produce Molecular Twisting and Möbius Aromaticity," Angew. Chem. Int. Ed., 2008, 47, 681-684, DOI: 10.1002/anie.200704407

InChIs

1(X=H): InChI=1/C30H22N6/c1-2-20-14-22-5-6-24(33-22)16-26-9-10-28(35-26)18-30-12-11-29(36-30)17-27-8-7-25(34-27)15-23-4-3-21(32-23)13-19(1)31-20/h1-18,31-32,35-36H/b19-13-,20-14-,21-13+,22-14-,23-15-,24-16-,25-15-,26-16-,27-17-,28-18+,29-17-,30-18-

InChIKey: LZQBSNZLFFXDHG-FXYKPCLQBX

1(X=CF₃): InChIKey: XMLQOLTZAIQLSA-UFROFZBYBD

2(X=H): InChI=1/C30H20N6/c1-2-20-14-22-5-6-24(33-22)16-26-9-10-28(35-26)18-30-12-11-29(36-30)17-27-8-7-25(34-27)15-23-4-3-21(32-23)13-19(1)31-20/h1-18,31,36H/b19-13-,20-14-,21-13-,22-14-,23-15-,24-16+,25-15+,26-16-,27-17-,28-18-,29-17-,30-18-

InChIKey: MMFGRQLRZMFRGC-NJRWMLEBBC

2(X=CF₃): InChIKey: FFCNJJQCGZCFGC-FJVZODTDBS

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.

	[α]D (expt)	[α]D (calc)
1	-52.7,a -60.5,b -44.6c	-38.8c
2	55.7d	10.5c
3	-60e	-20.6c
4	-110e	-220.8c

^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.

Wavelength (nm)	B3LYPa	CCSD(MVG)a	Expt.b
589	221.5	196.0	192.7
578	231.4	204.5	201.3
546	264.3	232.9	229.7
436	460.7	398.7	400.2
365	752.2	635.4	648.2

^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