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Keywords:

  • alkenes;
  • carbocations;
  • density functional calculations;
  • protonation;
  • terpenoids

Nature makes an astonishing array of complex terpenoid natural products from only a few simple achiral, acyclic precursors such as farnesyl pyrophosphate.1 Still, many details of terpenoid cyclization mechanisms are unknown. One outstanding issue is whether nonclassical carbocations are involved in these mechanisms,1, 2 and if so, then when, where, and why? During our ongoing theoretical studies on the mechanisms of terpenoid cyclizations, we encountered the unusual carbocation 1 (Figure 1).3, 4 In this complex cation, a formally tetracoordinate proton is seemingly suspended between two C[DOUBLE BOND]C bonds on opposite sides of a cyclooctadiene ring.

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Figure 1. Optimized (B3LYP/6-31+G(d,p)) geometry of cation 1 (C black, H white). Selected bond lengths (Å) are shown.

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Intrigued by this structure, we set out to explore simpler related species to see how common this structural motif might be. Initially we explored models based on 1,5-cyclooctadiene (2; Figure 2). Addition of a proton between its two C[DOUBLE BOND]C bonds followed by geometry optimization (using either B3LYP/6-31+G(d,p) or MP2/6-31+G(d,p)) led to cation 3 (Figure 3).4 The geometry of cation 3, which is D2-symmetric, is quite similar to the core of 1.5 The central proton of 3 is shared evenly by all four “alkene” carbon atoms at a distance of 1.48 Å (B3LYP level) or 1.46 Å (MP2 level) from each;6 C⋅⋅⋅H distances in both cyclic7 and acyclic8 three-center, two-electron [C⋅⋅⋅H⋅⋅⋅C]+ cations are less, typically around 1.3 Å. The double bonds in 2 appear to be well-preorganized to chelate a proton and are lengthened upon doing so as they share their electron density with the sandwiched proton. Overall, cation 3 can be viewed as a hybrid of the resonance structures shown in Scheme 1, a very unusual flavor of nonclassical cation9 that boasts a five-center, four-electron bonding array.

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Figure 2. Structure of cyclooctadiene 2. Selected bond lengths and distances (Å; B3LYP/6-31+G(d,p) (MP2/6-31+G(d,p) in parentheses)) are shown. ✶ indicates carbon atoms of doubly allylic bonds.

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Figure 3. Three views of cation 3. Selected bond lengths (Å; B3LYP/6-31+G(d,p) (MP2/6-31+G(d,p) in parentheses)) are shown.

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Scheme 1. Resonance structures for cation 3.

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Interestingly, both doubly allylic bonds (between carbon atoms marked with asterisks in Figure 2) of 2 are slightly lengthened upon addition of the proton, which indicates that they may help stabilize the four equivalent resonance structures shown in Scheme 1.10 If the limiting resonance structure, which is shown at the left of Scheme 2 and consists of a proton sandwiched between two butadienes, is a significant contributor, then we arrive at the very unusual resonance hybrid shown at the right of Scheme 2, a nine-center, eight-electron species.11, 12

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Scheme 2. Additional resonance structure (left; a proton sandwiched between two butadienes) and resulting resonance hybrid (right; a nine-center, eight-electron species) for 3.

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Let us now consider the distribution of charge throughout the molecule. Computed atomic charges13 are shown in Figure 4 a and the electrostatic potential of 3,14 mapped onto a surface that approximates the van der Waals surface of this species, is shown in Figure 4 b. The central proton is the most positive atom in 3, but positive charge is still delocalized over the molecule. In addition, it appears that access to the central proton is somewhat limited. The computed chemical shift of the central proton is also quite unusual with δ=+13.45 ppm (GIAO/B3LYP/6-31+G(d,p) level) or δ=+13.33 ppm (GIAO/MP2/6-31+G(d,p) level).15, 16 These chemical shift values are quite unlike those observed experimentally and computationally for protons in stable three-center, two-electron [C⋅⋅⋅H⋅⋅⋅C]+ cations, which typically range from δ=−7 to −3 ppm.8, 17 Clearly, whereas the hydrogens in [C⋅⋅⋅H⋅⋅⋅C]+ cations are quite electron-rich (hydride-like), the hydrogen in cation 3 is quite electron-deficient.

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Figure 4. a) Computed atomic charges (B3 LYP/6-31+G(d,p): CHelpG (NBO in parentheses)13), b) electrostatic potential surface constructed from the B3 LYP density (blue is most positive and red is least positive), and c) qualitative and computed (B3LYP/6-31+G(d,p), isovalue=0.04) molecular orbitals corresponding to the “butadienes+H” picture of bonding discussed in the text for cation 3. Relative sizes of component atomic orbitals are not considered in the qualitative picture.

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One qualitative approach to constructing the molecular orbitals of the nine-center array in 3 is to build them from combinations of the π orbitals of butadiene and the s orbital of a proton. This leads to the orbitals shown at the center of Figure 4 c. This qualitative picture is also reflected in the Kohn–Sham orbitals18 from our B3 LYP/6-31+G(d,p) calculations which are shown on the outside of Figure 4 c. Wiberg bond indices13c for the C⋅⋅⋅H bonds, partial Cequation imageC double bonds, and doubly allylic C[BOND]C bonds are 0.21, 1.65, and 0.94, respectively, and these values are most consistent with the five-center, four-electron picture described above (see Scheme 1).

What are the limits on forming cations such as 3?12 Although cation 3 is highly delocalized, protonation of cyclooctadiene 2 on the “outside” actually leads to a more stable isomer, 4 (Figure 5).19a Structure 4 is approximately 40 kcal mol−1 lower in energy than 3 (39.6 and 40.3 kcal mol−1 at the B3LYP/6-31+G(d,p) and MP2/6-31+G(d,p) levels, respectively), perhaps, at least in part, because 4 allows an alternative nonclassical (three-center, two-electron) bonding array to form. The barrier for rearrangement of 3 to 4, via the transition-state structure shown in Figure 6,4b is computed to be 2.8 kcal mol−1 at the B3LYP/6-31+G(d,p) level and 8.5 kcal mol−1 at the MP2/6-31+G(d,p) level.19b Note that, as expected for a very exergonic reaction, this is an early transition state, dominated by shifting of the proton. Note also that one of the doubly allylic bonds lengthens, which is indicative of hyperconjugative stabilization of the positive charge that builds up in its vicinity as the proton moves away from its central position. Whether or not suitably substituted systems that favor “in-protonation” or protect such “in-protonated” structures can be contrived is an open question.20, 21

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Figure 5. Computed geometry of the “out” protonated isomer 4. Selected bond lengths and distances (Å; B3LYP/6-31+G(d,p) (MP2/6-31+G(d,p) in parentheses)) are shown.

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Figure 6. Computed geometry of the transition state for the isomerization of 3 to 4. Selected bond lengths and distances (Å; B3LYP/6-31+G(d,p) (MP2/6-31+G(d,p) in parentheses)) are shown.

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The propensities of other 1,5-cyclooctadiene isomers to form cations such as 3 were also explored.12 First, there is another conformer of (E,E)-2. This structure, shown at the top of Figure 7, is less stable than 2 by 6.5 kcal mol−1 at the B3LYP/6-31+G(d,p) level and 7.9 kcal mol−1 at the MP2/6-31+G(d,p) level, and its two C[DOUBLE BOND]C bonds are parallel rather than “crossed” as they are in 2. This arrangement is also suitable for sandwiching a proton, and C2h-symmetric structure 5 is the energy-minimized structure of the resulting carbocation (Figure 8). Analogous delocalized cations could not, however, be located for E,Z and Z,Z isomers of 2 (Figure 7).22 This finding is consistent with the fact that the E,E isomers seem to be better preorganized to share a proton; that is, they have shorter distances between their double bonds.

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Figure 7. Computed geometries of cyclooctadienes. Selected bond lengths and distances (Å; B3LYP/6-31+G(d,p) (MP2/6-31+G(d,p) in parentheses)) are shown.

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Figure 8. Geometry of cation 5. Selected bond lengths (Å; B3LYP/6-31+G(d,p) (MP2/6-31+G(d,p) in parentheses)) are shown.

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In summary, we have described a new type of nonclassical carbocation with a tetracoordinate proton. While exotic in their appearance, such species might be formed from suitable cyclooctadienes or by rearrangements of other cations and may even play a role in some biosynthetic terpenoid cyclizations. We are exploring both of these possibilities.3 The prospect that such intermediates can lead to many different species through simple addition, rearrangement, or deprotonation reactions is particularly attractive from the perspective of reaction design.

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    P. Gutta, D. J. Tantillo, unpublished results. Preliminary calculations indicate that 1 lies on the pathway between the farnesyl cation and pentalenene, a polycyclic terpenoid natural product, at least in the absence of a surrounding enzyme (see Ref. [1] for background on this and related terpenoid cyclizations).
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    All calculations were performed with Gaussian 03 (Revision B.04), M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery, Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, J. A. Pople, Gaussian, Inc., Pittsburgh, PA, 2003;
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    Geometries were optimized without symmetry constraints using B3LYP/6-31+G(d,p) (A. D. Becke, J. Chem. Phys. 1993, 98, 56485652; A. D. Becke, J. Chem. Phys. 1993, 98, 13721377; C. Lee, W. Yang, R. G. Parr, Phys. Rev. B 1988, 37, 785789; P. J. Stephens, F. J. Devlin, C. F. Chabalowski, M. J. Frisch, J. Phys. Chem. 1994, 98, 11 62311 627) and MP2/6-31+G(d,p) (C. Møller, M. S. Plesset, Phys. Rev. 1934, 46, 618622). All structures were characterized by frequency calculations, and reported energies include zero-point energy corrections (unscaled). Intrinsic reaction coordinate (IRC) calculations (C. Gonzalez, H. B. Schlegel, J. Phys. Chem. 1990, 94, 55235527 and K. Fukui, Acc. Chem. Res. 1981, 14, 363368) were also used to verify the identity of the transition structure associated with the interconversion of 3 and 4;
  • 4c
    Extremely similar results (for both geometries and relative energies) were obtained by using the 6-311+G(d,p) basis set. For example, for cation 3, the biggest change in bond lengths on going from the double-zeta to triple-zeta basis set was 0.004 Å with both B3LYP and MP2, and predicted barriers for the 3-to-4 rearrangement changed by less than 0.5 kcal mol−1 for each. See Supporting Information for additional details;
  • 4d
    For recent reports that compare the B3LYP and MP2 methods for computing geometries and relative energies of small three-center, two-electron cations, see: I. V. Vrcek, V. Vrcek, H.-U. Siehl, J. Phys. Chem. A 2002, 106, 16041611 and D. Farcasiu, P. Lukinskas, S. V. Pamidighantam, J. Phys. Chem. A 2002, 106, 11 67211 675;
  • 4e
    Structural drawings were produced by using Ball & Stick (N. Müller, A. Falk, Ball & Stick V.3.7.6—Molecular Graphics Application for MacOS Computers, Johannes Kepler University, Linz, 2000).
  • 5
    Many complexes of cyclooctadienes with transition metals are known. For structurally characterized complexes with simple metal cations, see:
  • 5a
    with Ag+: A. Albinati, S. V. Meille, G. Carturan, J. Organomet. Chem. 1979, 182, 269274;
  • 5b
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  • 6
     
  • 6a
    Computations on related complexes of protons with simple alkenes and alkynes were recently described. In these systems, the protons were shared quite unsymmetrically between the two π systems. See: S. J. Grabowski, W. A. Sokalski, J. Leszczynski, J. Phys. Chem. A 2004, 108, 18061812;
  • 6b
    A tricyclic tetraamine that complexes a proton by means of an array of four nitrogen lone-pairs has also been described. See: S. T. Howard, I. A. Fallis, J. Org. Chem. 1998, 63, 71177119;
  • 6c
    See also: J. W. M. Carneiro, C. A. Taft, C. H. T. P. Silva, J. G. R. Tostes, P. R. Seidl, P. S. S. Sinto, V. E. U. Costa, J. Alifantes, Chem. Phys. Lett. 2001, 345, 189194.
  • 7
     
  • 7a
    W. Quapp, D. Heidrich, J. Mol. Struct.: THEOCHEM. 2002, 585, 105117, and references therein;
  • 7b
    J. W. de M. Carneiro, P. v. R. Schleyer, M. Saunders, R. Remington, H. F. Schaefer III, A. Rauk, T. S. Sorensen, J. Am. Chem. Soc. 1994, 116, 34833493;
  • 7c
    M. D. Bojin, D. J. Tantillo, unpublished results.
  • 8
     
  • 8a
    R. Ponec, G. Yuzhakov, D. J. Tantillo, J. Org. Chem. 2004, 69, 29922996;
  • 8b
    J. E. McMurry, T. Lectka, J. Am. Chem. Soc. 1993, 115, 10 16710 173;
  • 8c
    J. Cioslowski, J. Am. Chem. Soc. 1993, 115, 51775179.
  • 9
    For leading references, see:
  • 9a
    C. A. Grob, Acc. Chem. Res. 1983, 16, 426431;
  • 9b
    H. C. Brown, Acc. Chem. Res. 1983, 16, 432440;
  • 9c
    G. A. Olah, G. K. S. Prakash, M. Saunders, Acc. Chem. Res. 1983, 16, 440448;
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    C. Walling, Acc. Chem. Res. 1983, 16, 448454;
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    H. C. Brown, The Nonclassical Ion Problem, Plenum, New York, 1977 (with comments by P. von R. Schleyer).
  • 10
    Note that the doubly allylic bonds in 2 are already rather long, presumably as a result of through-bond coupling between the two alkenes. For leading references on through-bond coupling in related systems, see:
  • 10a
    H. Gan, M. G. Horner, B. J. Hrnjez, T. A. McCormack, J. L. King, Z. Gasyna, G. Chen, R. Gleiter, N. C. Yang, J. Am. Chem. Soc. 2000, 122, 12 09812 111;
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    R. Gleiter, W. Schäfer, Acc. Chem. Res. 1990, 23, 369375.
  • 11
     
  • 11a
    This species can also be thought of as a σ-polyacene with a proton sandwiched between its two polyene chains. For details on σ-polyacenes, see: D. J. Tantillo, R. Hoffmann, K. N. Houk, P. W. Warner, E. C. Brown, D. K. Henze, J. Am. Chem. Soc. 2004, 126, 42564263;
  • 11b
    In addition, 3 can be thought of as a protonated version of a suprafacial–suprafacial transition state for [4+4] dimerization of butadiene. For a recent discussion on the protonation of pericyclic transition structures, see: R. Hoffmann, D. J. Tantillo, Angew. Chem. 2003, 115, 60576062; Angew. Chem. Int. Ed. 2003, 42, 58775882.
  • 12
     
  • 12a
    Addition of methoxy groups to all four carbon atoms of the doubly allylic bonds results in a structure which is similar to that of 3, but with slightly lengthened (1.652 Å) doubly allylic bonds;
  • 12b
    The following structure, 6chemical structure image, has also been shown to contain a tetracoordinate proton; P. von R. Schleyer, personal communication after this manuscript was submitted.
  • 13
    Charge computations and NBO (natural bond orbital) analysis were carried out for the B3LYP/6-31+G(d,p) structures.
  • 13a
    CHelpG: C. M. Breneman, K. B. Wiberg, J. Comput. Chem. 1990, 11, 361373;
  • 13b
    NBO: A. E. Reed, L. A. Curtiss, F. Weinhold, Chem. Rev. 1988, 88, 899926 and “Natural Bond Orbital Methods”, F. Weinhold in Encyclopedia of Computational Chemistry, Vol. 3 (Eds.: P. v. R. Schleyer, N. L. Allinger, T. Clark, J. Gasteiger, P. A. Kollman, H. F. Schaefer III, P. R. Schreiner), Wiley, Chichester, 1998, pp. 17921811;
  • 13c
    Wiberg bond indices: K. B. Wiberg, Tetrahedron 1968, 24, 10831096.
  • 14
     
  • 14a
    C. K. Bagdassarian, V. L. Schramm, S. D. Schwartz, J. Am. Chem. Soc. 1996, 118, 88258836;
  • 14b
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  • 15
    Chemical shift calculations and geometry optimizations were performed at the same level of theory. For details on the methodology used, see:
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    K. Wolinski, J. F. Hinton, P. Pulay, J. Am. Chem. Soc. 1990, 112, 82518260;
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    K. Wolinski, R. Haacke, J. F. Hinton, P. Pulay, J. Comput. Chem. 1997, 18, 816825;
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    For a classic example of the use of computed chemical shifts in the characterization of carbocation structures, see: P. von R. Schleyer, K. Laidig, K. B. Wiberg, M. Saunders, M. Schindler, J. Am. Chem. Soc. 1988, 110, 300301;
  • 15d
    For additional details on the successes and failures of DFT (density functional theory) in predicting magnetic properties, see: Calculation of NMR and EPR Parameters: Theory and Applications (Eds.: M. Kaupp, M. Bühl, V. G. Malkin), Wiley, New York, 2004.
  • 16
    The computed chemical shifts for all of the other protons in 3 ranged between δ=+3.08 and +6.16 ppm at the B3LYP/6-31+G(d,p) level (+2.99 and +5.93 ppm at the MP2/6-31+G(d,p) level). All values are referenced to that for the protons in tetramethylsilane (δ=0.00 ppm).
  • 17
     
  • 17a
    D. J. Tantillo, R. Hoffmann, J. Am. Chem. Soc. 2003, 125, 40424043;
  • 17b
    A referee suggested that the chemical shifts at δ=+13 ppm might be indicative of antiaromaticity. The NICS(1) (nucleus-independent chemical shift at 1 Å above) value above the central proton is computed to be −5.4 ppm, and the NICS(0) and NICS(1) values at and above the centroid of the C⋅⋅⋅H⋅⋅⋅C rings are computed to be −41.4 and −3.3 ppm, all at the GIAO/B3LYP/6-31+G(d,p) level. These values suggest that, if anything, this bonding array is slightly aromatic (the value at the centroid of the C-H-C rings is likely so large due to the proximity of the ring bonds). The NICS method is described in: P. von R. Schleyer, C. Maerker, A. Dransfeld, H. J. Jiao, N. J. R. v. E. Hommes, J. Am. Chem. Soc. 1996, 118, 63176318 and P. von R. Schleyer, M. Manoharan, Z.-X. Wang, B. Kiran, H. Jiao, R. Puchta, N. J. R. v. E. Hommes, Org. Lett. 2001, 3, 24652468.
  • 18
    R. Stowasser, R. Hoffmann, J. Am. Chem. Soc. 1999, 121, 34143420.
  • 19a
    For an excellent review on “in–out” isomerism see: R. W. Alder, S. P. East, Chem. Rev. 1996, 96, 20972111;
  • 19b
    The possibility that tunneling may contribute to rearrangements of 3 was suggested by a referee. However, additional calculations will be required to test this proposition.
  • 20
    Note that the computed proton affinity of 2 (to form 3) is 182.8 kcal mol−1 at the B3LYP/6-31+G(d,p) level, considerably larger than values for normal alkenes, which are typically around 165 kcal mol−1. See Ref. [11b] as well as F. A. Carroll, Perspectives on Structure and Mechanism in Organic Chemistry, Brooks/Cole, Pacific Grove, 1998, and references therein.
  • 21
    There is also an analogy between 3 and the well-known bis-amine “proton sponges” in that they both chelate protons. For reviews on “proton sponges”, see:
  • 21a
    H. A. Staab, T. Saupe, Angew. Chem. 1988, 100, 895909; Angew. Chem. Int. Ed. Engl. 1988, 27, 885887;
  • 21b
    A. L. Llamas-Saiz, C. Foces-Foces, J. Elguero, J. Mol. Struct. 1994, 328, 297323; See also Ref. [6].
  • 22
    The energies of the E,Z and Z,Z isomers, relative to that of 2, are −3.1 and −22.9 kcal mol−1 at the B3LYP/6-31+G(d,p) level and +1.1 and −18.9 kcal mol−1 at the MP2/6-31+G(d,p) level, respectively.

Supporting Information

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  2. Supporting Information

Supporting information, which includes coordinates and energies for all structures, for this article is available on the WWW under http://www.wiley-vch.de/contents/jc_2002/2005/z461915_s.pdf or from the author.

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