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Metalla-Cope Rearrangements: Bridging Organic and Inorganic Chemistry† Edyta M. Greer* Department of Natural Sciences, Baruch College, the City UniVersity of New York, 17 Lexington AVenue, New York, New York 10010
Roald Hoffmann Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell UniVersity, Ithaca, New York 14853 ReceiVed: December 23, 2009; ReVised Manuscript ReceiVed: February 2, 2010
Density functional theory calculations are performed to explore both concerted chairlike and boatlike as well as stepwise mechanisms of the Cope rearrangement of two hypothetical metalladienes. An osma-1,5-hexadiene is designed by substituting CH2 in 1,5-hexadiene by its isolobal analogue, 16-electron Os(PH3)4. The energy of activation corresponding to the rearrangement of osma-1,5-hexadiene involving the chairlike saddle point is computed as 37.4 kcal/mol, 3.9 kcal/mol above the energy barrier of the parent 1,5-hexadiene calculated with the same method and basis set, and is 4.5 kcal/mol below that of the boatlike pathway. In another isolobal replacement, the CH in 1,5-hexadiene is substituted by a 15-electron Re(PH3)3 fragment. Now the chairlike rearrangement of the rhenia-1,5-hexadiene has an Ea value of 23.0 kcal/mol, 10.8 kcal/mol less than the energy barrier of the parent 1,5-hexadiene calculated at the same level of theory. The ring inversion of the chair and osma-chair diradical intermediates of the stepwise reaction pathway is also examined and is found in both cases to proceed through a very flat potential energy surface involving twist intermediates. Introduction Much clever experiment and theory has focused on a fundamental hydrocarbon reaction, the Cope rearrangement.1 One mechanism for this [3,3]-sigmatropic rearrangement of 1,5hexadiene 1A and 1B follows a concerted path involving chairlike, 2, and boatlike, 3, transition states, respectively.2 Labeling experiments revealed that the chairlike pathway, with its experimentally determined energy of activation, Ea ) 33.5 ( 0.5 kcal/mol, is favored over the boatlike pathway by 11 kcal/mol.3 The Cope rearrangement may also follow a stepwise mechanism that formally traverses the diradical intermediate cyclohexane-1,4-diyl (4).2
It has also been postulated4 and confirmed by measurements of secondary kinetic isotope effects5 that it is useful to regard †
Part of the “Klaus Ruedenberg Festschrift”.
the transition structure of the Cope rearrangement actually as a continuum of aromatic TS 3, diradical 4, and coupled allyl structures (5) changing in response to the substituent pattern at C(2) and C(5), as well as at C(1), C(3), C(4), and C(6).6 Thus, the Cope rearrangement has been called chameleonic.4 The extended debate surrounding the mechanism of the Cope rearrangement has led to much theoretical soul-searching, and instructive experience in the calculation of reactivity.7 The basic structural requirement for the Cope rearrangement is the presence of π bonds in the 1,5-positions. Thus, the Bergman cyclization of 1,5-hexadiyne (6A) leading to the diradical intermediate (6B) via the rearrangement of the in-plane/ radial π-bonds of the alkynes (and not the remaining π-bonds) can be viewed as a Cope-type rearrangement following the stepwise mechanism.8
In previous work, we studied theoretically an interesting variant of the Bergman rearrangement, in which a C was replaced by an isolobal metal fragment, for instance, Os(PH3)3.9 The outcome was a significant decrease of the energy barrier corresponding to the rearrangement of the metallaenediyne. This prompted us to explore in this paper the effect of metal centers on the parent Cope rearrangement of 1,5-hexadienes.
10.1021/jp912131w 2010 American Chemical Society Published on Web 03/01/2010
Metalla-Cope Rearrangements Methods All calculations were carried out with Gaussian 03.10 The energetics of the chairlike and boatlike concerted rearrangement of all hydrocarbon 1,5-hexadiene and the conformational inversion of the diradical 4 were calculated using the B3LYP functional11 and the 6-31G*12 basis set,7a,h,13-15 supported by B3LYP/SDD11,16 calculations for selected geometries.9,17 Reactants, transition structures, and products involved in the chairlike and boatlike concerted Cope rearrangement of the metal-center-containing 1,5-hexadiene were optimized at the B3LYP/SDD level. Calculations of the stepwise mechanism of the Cope and the metalla-Cope rearrangement involving diradicals and their interconversion require special care due to the essential role of correlation in the system.7g,15,18-24 These calculations were carried out with the unrestricted B3LYP11 method and a SDD16 basis set with the “guess ) (mix, always)” option14 applied in the route section of the Gaussian 03 input file. In accounting partially for static electron correlation, this way of calculating singlet diradicals introduces spin contamination, which can be gauged by the value of 〈S2〉.17 The methodology is also less computationally demanding, compared to multiconfigurational and multireference methods often used for calculations of much smaller systems than the metalladiradicals studied herein. The values of 〈S2〉 corresponding to singlet and triplet diradicals obtained from the output files before spin annihilation are reported throuhout this paper. Spin corrections were performed on the singlet spin-contaminated systems using values of 〈S2〉 before spin annihilation to provide energies of the pure singlet.15,19,20 All closed-shell stationary points (minima and first order saddle points) were characterized by frequency calculations and include unscaled zero point energy corrections derived from frequency calculations. The reversed and forward intrinsic reaction coordinate (IRC) calculations were carried out for all transition structures.26 In all investigated cases, geometries of the starting materials and products were determined by optimizing structures derived from IRC calculations. The stability of the restricted wave functions computed for the molecular systems involved in the chairlike and boatlike concerted pathways was examined by reoptimizing all of the stationary points using the “guess ) (mix, always)” option in the route section. The stability of the unrestricted wave function corresponding to the various cyclohexane-1,4-diyl and metallacyclohexane-1,4-diyl diradicals was verified by using the “SCF ) Tight”, “stable ) opt”, and “guess ) mix” options as incorporated in the “route” section. A command “stable )o pt” allows one to reoptimize the wave function to the lowest energy solution of the SCF equations, should any instability be found.26 The checkpoint files from these calculations and the “guess ) read” option used in the route section were used for the frequency calculations of the open-shell stationary points. The energy of triplets was computed at the geometry of the broken spin diradical singlet state. All DFT calculations were performed with an integration grid UltraFine, recommended for molecules containing many tetrahedral centers, such as PH3.25 All structures were visualized with GaussView (version 3.09).27 The Parent System at the B3LYP/6-31G* and B3LYP/ SDD Levels of Theory Numerous theoretical studies of the Cope rearrangement led to the conclusion that the combination of the B3LYP method and 6-31G* basis set reproduces the experimental results with
J. Phys. Chem. A, Vol. 114, No. 33, 2010 8619 excellent agreement.7d,e,13,14 Our calculations show that the energy barrier for the chairlike Cope rearrangement calculated at the B3LYP/6-31G* level is 33.5 kcal/mol,7d the same as the experimentally determined energy of activation.3 At the same level of theory, passage over the boatlike transition structure costs 41.6 kcal/mol, 2.9 kcal/mol less than the experimentally observed3 Ea and 8.1 kcal/mol more than the rearrangement involving a chairlike transition structure. The intermediate diradical 4 involved in the stepwise mechanism is 5.5 kcal/mol less stable than the chairlike transition structure of the concerted mechanism at the same level of theory. The 〈S2〉 value of 4 at B3LYP/6-31G* is 0.90, indicating a large degree of the spin contamination from the higher triplet state.28 We also tested the performance of the B3LYP/SDD method for modeling of the Cope rearrangement of the parent system. With this combination of method and basis set, we calculated an activation energy of 33.8 kcal/mol, 0.3 kcal/mol above the Ea computed at B3LYP/6-31G*, for the chairlike and of 41.0 kcal/mol, 0.6 kcal/mol higher than the Ea calculated at B3LYP/ 6-31G* for the boatlike rearrangement. The diradical intermediate 4, 〈S2 ) 0.93〉, involved in the stepwise mechanism, is 6.5 kcal/mol above the chairlike transition structure. These results are in very good agreement with results obtained with B3LYP/ 6-31G*. The positive experience with B3LYP/SDD calculations applied to model the Cope rearrangement of the parent system as well as with various metalla-Bergman rearrangements9 prompted us to use this combination of method and basis set to study the rearrangements of the metal-containing 1,5-hexadienes. Effects of 16-Electron Os(PH3)4 on the Cope Rearrangement To gain some insight on the nature of the metalla-Cope rearrangement of the metal-containing 1,5-hexadienes, we started with the rearrangement of osma-1,5-hexadiene (7). The isolobal
analogy points to a resemblance of the frontier orbitals of inorganic and organic fragments.29 Such an analogy exists between CH2 and a d8 ML4 fragment; it is this reasoning that led us to organometallic complex 7. In it, the 6-electron CH2 fragment in the parent all-hydrocarbon system is replaced by its isolobal analogue, the 16-electron metal fragment of Os(PH3)4. From another perspective, in complex 7, the metal is coordinated by four 2e σ donor phosphines, a vinyl anion (:CHdCH2)- and allyl anion (:CH2sCHdCH2)- ligands. Our DFT calculations predict OssC(H) and OssC(H2) bond distances to be 2.11 and 2.22 Å, respectively; these are reasonable values for Os to a carbenoid and an alkyl carbon bond. The Os-C(vinyl) bond distance is on the higher end of the range from 1.897(4) Å30 through 2.063(10) Å31 to 2.115(9) Å32 reported in the literature. The value of the Os-C alkyl group distance is close or comparable to those observed for the Os-C methyl group (2.196(4), 2.199(4), and 2.218(3) Å).33
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The ligands are arranged in a slightly distorted octahedral geometry. The computed value of the energy of activation corresponding to rearrangement of 7 is 37.4 kcal/mol, only 3.9 kcal/mol higher than the energy barrier for the rearrangement of the parent Cope system computed at the same level of theory and determined experimentally. The process is endothermic by 13.3 kcal/mol. In the chairlike transition structure (TS 8), which in analogy to 2 is expected to be aromatic due to the extent of electron delocalization, the breaking Os-C and the forming C-C bonds are 2.61 and 1.87 Å, respectively. The corresponding distances in the transition structure 2 (relative to the rearrangement of the parent 1,5-hexadiene 1A) are 2.00 Å. Of course, introduction of the metal center destroys the C2V symmetry in transition state 2; the consequent asymmetry of bond lengths (one M-C, the other C-C) is expected. The successful location of the transition structure TS 8 was confirmed by performing intrinsic reaction coordinate (IRC) calculations, which revealed that TS 8 connects 7 with another osma-1,5-hexadiene (9). This product of the rearrangement, 9, has a slightly distorted trigonal bipyramidal geometry with the formal carbene ligand :CHsCH2sCH2sCHdCH2 occupying an equatorial position. Complex 9 can in principle undergo Berry pseudorotation, a polytopal rearrangement characteristic of pentacoordinate species.34 The Berry pseudorotation of 9 gives rise to two trigonal bipyramids and two square pyramids; when we examined these, they collapsed to 9 during geometry optimization. We also examined the stepwise mechanism involving osmacyclohexane-1,4-diyl diradical (10). The calculated spin expec-
Greer and Hoffmann
Figure 1. The metalla-Cope rearrangement of 7 following the chairlike TS 8. For clarity, hydrogens were removed from phosphines.
The presence of the metal center in the intermediate 10 makes it asymmetric. Therefore, there are two different transition structures that connect the diradical intermediate 10 with the reactant and product. We were not able to locate transition structures associated with the ring-opening of the intermediate 10 to yield a reactant or a product. All attempts to predict both transition structures associated with the ring-opening of 10 led to the transition structure TS 8 of the concerted mechanism (Figure 1). This suggests a great structural and energetic similarity of these transition structures to TS 8, and indicates that the barrier corresponding to these processes is comparable to the energy barrier corresponding to the rearrangement of 7 through 8. Conformational Inversion of the Chair Cyclohexa-1,4-diyl Diradical: Not a Simple Story
tation value 〈S2〉 ) 0.85 for the reaction intermediate, metalladiradical 10, obtained before spin annihilation, indicates a significant spin contamination of its singlet state by a higher triplet spin state. Compound 10 is only 0.2 kcal/mol less stable than TS 8. The energy of the triplet state diradical (〈S2〉 ) 2.01, before the spin annihilation) obtained from the singlet point calculation at the optimized geometry of the mixed singlet metalladiradical 10 is 3.3 kcal/mol higher than that of the mixed singlet spin state. The S-T energy difference discussed above is known as the vertical singlet-triplet gap. The vertical S-T gap is 1.8 kcal/mol greater than the adiabatic S-T gap that can be obtained for the singlet and the geometry optimized triplet. It is possible to obtain improved, pure S-T energy gaps by application of the approximate spin correction procedure proposed by Yamaguchi and co-workers.20,21 The use of the spincorrection procedure lowers the energy of the singlet metalladiradical by 2.4 kcal/mol compared to the spin-uncorrected species, and drops the energy of the diradical 10 below that of the transition state TS 8 for concerted rearrangement. The pure S-T energy gap is thus estimated computationally as 5.7 kcal/ mol; the singlet coming lower indicates interaction between the radical centers.
The organic diradical parent to the organometallics we are studying, the hydrocarbon cyclohexa-1,4-diyl, incorporates two sp2 centers into a six-remembered ring. Such a system would be expected to lie on an easy pseudorotation surface, a process on the face of it unrelated to its diradical character. The analogy would be to cyclohexa-1,4-dione (11)35 or dicarbonium ion (12) in a six-membered ring. The potential energy surfaces of these organic systems are instructive, in suggesting to us potential geometries (and computational pitfalls) in our organometallics.
The cyclohexa-1,4-diyl diradical 4 itself has been the subject of several investigations;7a,36-38 the fascinating story of this diradical is sketched in the Supporting Information. We studied the ring inversion/pseudorotation of 4 at the uB3LYP level using 6-31G* and SDD basis sets. Figure 2 summarizes our results for the cyclohexa-1,4-diyl system obtained with uB3LYP/SDD. We found that the chair form of cyclohexa-1,4-diyl undergoes conformational inversion, which occurs by easy rotation about
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Figure 2. Ring inversion/pseudorotation of the single chair cyclohexa-1,4-diyl diradical. Values in italics were obtained at the uB3LYP/SDD level of theory. Energies are given in kcal/mol, and bond distances are given in Å.
Figure 3. uB3LYP/SDD PES for the inversion of the osma-chair. Energies and bond distances are reported in kcal/mol and Å, respectively.
C-C bonds in analogy to cyclohexane39 and gives a very flat potential energy surface which can be described as a “twixtyl”40 or “caldera”.41 Detailed discussion of the PES corresponding to the interconversion of 4 with uB3LYP/SDD, along with the surface obtained with uB3LYP/6-31G*, may be found in the Supporting Information. Conformational Transformations of the Chair Osma-Cyclohexa-1,4-diyl Diradical The surface for the osma-substituted diradical 10 is more complicated, for it superimposes a major electronic perturbation on top of the pseudorotation just described. We attempted to investigate this system by taking various points along a hydrocarbon pseudorotation path, putting in the Os fragment, and reoptimizing. We label the metalladiradical structures as osma-chair, osma-boat, etc., by analogy to the parent cyclohexadienyl and cyclohexane structures. The results are summarized in Figure 3. We found that the osma-chair A diradical (〈S2〉 ) 0.85) undergoes inversion involving the osma-half-twist A (〈S2〉 ) 1.01) to yield the osma-twist A (〈S2〉 ) 1.00). The energy barrier corresponding to this process is 6.3 kcal/mol, 3.8 kcal/mol higher than the Ea predicted for the rearrangement of the parent chair at the same level of theory. The osma-twist A is 2.5 kcal/mol above the osma-chair A. The twist form can either move “back” to the osma-chair A (Ea ) 3.8 kcal/mol) or forward to the new osma-twist B (〈S2〉 ) 0.98). The forward inversion costs only 2.3 kcal/mol, 3.9 kcal/mol less than the equivalent inversion of the all-hydrocarbon system predicted at the same level of theory, and it involves the osma-boat transition structure (〈S2〉 ) 1.00).
The new osma-twist B can transform into the final osma-chair B (〈S2〉 ) 0.75) by overcoming an energy barrier of 8.2 kcal/ mol. The final osma-chair B is 0.1 kcal/mol more stable than the starting osma-chair A. The general appearance of the pseudorotation surface of the metalladiradical is not that different from the all-hydrocarbon parentsthe half-twist waypoints are relatively higher in energy and the boat form lower in the osma-diradical. With these results in hand, we proceed to look at the effect of the metal fragment on the concerted mechanism of the Cope rearrangement involving the boatlike type transition structure 3. In this case, the rearrangement begins with the osma-1,5hexadiene (13).
Optimized complex 13 has a slightly distorted octahedral geometry at the metal center. The Os-Cvinylic and Os-Callylic bond distances are 2.12 and 2.24 Å, respectively (Figure 4), very similar, as expected, to the corresponding distances in 7, the starting point for the chair rearrangement of the osma1,5-hexadiene. The energy of activation corresponding to the rearrangement of 13 is 41.9 kcal/mol (Figure 4). The rearrangement involving 13 is endothermic by 10.1 kcal/mol.
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Greer and Hoffmann
Figure 4. The metalla-Cope rearrangement of 13.
TS 14 has C1 symmetry due to the presence of the metal center. The breaking σ Os-C and the forming σ C-C in TS 14 are 3.01 and 2.10 Å, respectively. (The breaking and forming σ C-C bonds in 2 calculated at the same level of theory are equal in length, 2.10 Å.) The product of rearrangement, another osma-1,5-hexadiene (15), has trigonal bipyramidal geometry at the metal center. The 〈S2〉 value of transition structure TS 14 is 0.00, implying a pure closed shell singlet state. At first sight, compound 13 resembles complex 7, the starting point for the chair TS rearrangement. The geometrical difference between the two is expressed by the distinct values of the C(2)-Os(3)-C(4)-C(5) dihedral angle in the two molecular systems. In compound 7, that dihedral angle is 116.0°, whereas, in compound 13, it is 33.5°. This difference in the value of the C(2)-Os(3)-C(4)-C(5) dihedral angle between 13 and 7 is connected with compounds 13 and 7 following boatlike and chairlike pathways, respectively. Compounds 7 and 13 are structural isomers, and that gave us an opportunity to examine the energies for structures involved in their rearrangement on the same energy scale (Figure 5; we related energies of all structures shown in Figure 1 to 4). As Figure 5 shows, compound 13 is by 2.8 kcal/mol less stable than 7. Both complexes were characterized by the frequency calculations as minima on the corresponding potential energy surface. The product of the chairlike rearrangement, complex 9, is more stable than the product of the boatlike rearrangement, 15, but only by 0.3 kcal/mol. Both complexes, 9 and 15, are trigonal bipyramidal at the metal center. The transition structure TS 14 connecting 13 and 15 is 7.2 kcal above TS 8 that marks the top of the PES of the rearrangement of 7. This energy difference between TS 8 and TS 14 and the fact that the Ea value of the boatlike rearrangement 13 f TS 14 f 15 is 4.5 kcal/mol above the energy barrier corresponding to the chairlike rearrangement 7 f TS 8 f 9 renders the rearrangement of 13 more demanding in energy than rearrangement of 7. This also follows the trend observed for the Cope rearrangement of the parent system, where the Ea corresponding to the boatlike rearrangement is 7.2 kcal/mol, as calculated with the B3LYP/ SDD method. The Effect of 15-Electron Re(PH3)4 Replacing CH on the Cope Rearrangement We also tried to replace 5-electron CH in the molecule of 1,5-hexadiene by its isolobal analogue, 15-electron Re(PH3)4.
Figure 5. Comparison of the computed energies of the chairlike metalla-Cope rearrangement of 7 vs the boatlike metalla-Cope rearrangement of 13 on the same energy scale; energy in kcal/mol.
Figure 6. The metalla-Cope rearrangement of 16.
This led us to rhenia-1,5-hexadiene (16). The choice of a d7 rhenium fragment allowed us to maintain one type of ligand coordinated to the transition metal center, reducing isomer complexity. It also made it possible to retain the octahedral geometry of the complex 16, again avoiding some complexity, in this case from potential polytopal rearrangements such as the Berry pseudorotation in the product. The concerted chairlike metalla-Cope rearrangement of 16 is explored in Figure 6. The formally d8 Re+ in the starting material 16 is surrounded by four phosphines, carbene (:CH2), and the C4H7- anion. The ResC(H2) and RedC(H2) bond distances in 16 are 2.23 and 1.94 Å, respectively. Compound 16 has a slightly distorted octahedral geometry at the metal center. The activation energy corresponding to the rearrangement of 16 is only 23.0 kcal/ mol, which is 10.8 kcal/mol lower than the Ea value of the rearrangement for the parent, all hydrocarbon 1,5-hexadiene calculated with the same method and basis set. The rearrangement of 16 yields its enantiomer, rhena-1,5-hexadiene 18. In addition to the significant decrease of the energy barrier corresponding to the chairlike Cope rearrangement of rhena1,5-hexadiene 16, the presence of the rigid metal fragment distorts the geometry of the transition structure (TS 17) in
Metalla-Cope Rearrangements comparison to 2. The geometry of TS 17 is reminiscent of the half-chair form.
The geometrical difference is also reflected in the substantially reduced interallylic distance in TS 17. In the transition structure TS 17, the bond distance between the methylene groups is 1.75 Å, shortened by 0.25 Å compared to the corresponding distance in the parent chairlike transition structure 2. The bonding in TS 17 resembles that in cyclohexane-1,4-diyl more than in an aromatic transition structure. This might be a further indication of the chameleonic nature of the transition structure for the Cope rearrangement. The computed 〈S2〉 value for TS 17 is 0.00. The restricted and unrestricted energies corresponding to TS 17 are the same, confirming the stability of the wave function. W. T. Borden has suggested to us that thermodynamics is responsible for the finding that substitution of Re(PH3)3 for C(2)-H of 1,5-hexadiene lowers the barrier to the Cope rearrangement by 10.8 kcal/mol. In TS 17, a weak Re-C π bond is broken, while a much stronger C(1)-C(6) σ bond is made. That is the reason why the two interallylic C-C bond lengths in TS 17 are considerably shorter than those in the Cope rearrangement of the hydrocarbon.42 Further theoretical investigations could not find the boatlike metalla-Cope rearrangement of the rhena-1,5-hexadiene. All approaches to a boatlike transition structure led to TS 17. We believe that this is due to the rigidity of the Re(PH3)4 metal fragment and the effect of steric interactions between ligands at the metal and H at the vinylic carbon at the adjacent all hydrocarbon allyl fragment. We were also unable to determine the geometry of the chair rhena-cyclohexane-1,4-diyl diradical involved in the stepwise mechanism of the metalla-Cope rearrangement. Concluding Comments The replacement of carbon by the metal center in 1,5hexadiene increases slightly the activation energy of the chairlike Cope rearrangement and decreases negligibly the Ea value of the boatlike Cope rearrangement, compared to the corresponding activation energies of the parent system calculated at the same level of theory. The replacement of 15-electron Re(PH3)4 for the 5-electron sCHd fragment in 1,5-hexadiene provides more stabilization. The energy of activation for the chairlike rearrangement of rhena-1,5-hexadiene 16 is decreased by 10.8 kcal/ mol. It would be interesting to see metal-containing derivatives of the parent 1,5-hexadiene synthesized and to determine the energies of activation for their metalla-Cope rearrangements. Acknowledgment. We dedicate this paper to Klaus Ruedenberg, a theoretician with remarkable insight. We gratefully acknowledge Baruch College and the CUNY Graduate Center computational facility for support and thank D. J. Tantillo, C. A. Parish, and K. Laane for stimulating discussions. We thank K. Ramig for the picture of the bridge at Lake Treman. The work
J. Phys. Chem. A, Vol. 114, No. 33, 2010 8623 at Cornell University was supported by NSF Research Grant CHE-0613306. Supporting Information Available: Details on computations including the PES corresponding to the ring inversion/ pseudorotation of the single chair cyclohexa-1,4-diyl diradical obtained at the uB3LYP/6-31G* and uB3LYP/SDD levels of theory; relative energies of the conformers of cyclohexa-1,4diyl predicted with B3LYP-6-31G*; Cartesian coordinates, absolute energies, spin expectation values 〈S2〉, and number of imaginary frequencies of all presented stationary points; details on a spurious cyclohexane-1,4-diyl intermediate; the complete list of authors for ref 10. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Cope, A. C.; Hardy, E. M. J. Am. Chem. Soc. 1940, 62, 441–444. (2) Gajewski, J. J. Hydrocarbon Thermal Isomerizations; Academic Press: New York, 1981. (3) Goldstein, M. J.; Benzon, M. S. J. Am. Chem. Soc. 1972, 94, 7147– 7149. (4) Doering, W. v. E.; Wang, Y. J. Am. Chem. Soc. 1999, 121, 10112– 10118. (5) Gajewski, J. J.; Conrad, N. D. J. Am. Chem. Soc. 1979, 101, 6693– 6704. (6) (a) Hrovat, D. A.; Beno, B. R.; Lange, H.; Yoo, H.-Y.; Houk, K. N.; Borden, W. T. J. Am. Chem. Soc. 1999, 121, 10529–10537. (b) Staroverov, V. N.; Davidson, E. R. J. Am. Chem. Soc. 2000, 122, 7377–7385. (c) Blavins, J. J.; Cooper, D. L.; Karadakov, P. B. J. Phys. Chem. A. 2004, 108, 194–202. (d) Siebert, M. R.; Tantillo, D. J. J. Am. Chem. Soc. 2007, 129, 8686–8687. (7) (a) Dewar, M. J. S.; Ford, G. P.; McKee, M. L.; Rzepa, H. S.; Wade, L. E. J. Am. Chem. Soc. 1977, 99, 5069–5073. (b) Osamura, Y.; Kato, S.; Morokuma, K.; Feller, D.; Davidson, E. R.; Borden, W. T. J. Am. Chem. Soc. 1984, 106, 3362–3363. (c) Dupuis, M.; Murray, C.; Davidson, E. R. J. Am. Chem. Soc. 1991, 113, 9756–9759. (d) Wiest, O.; Black, K. A.; Houk, K. N. J. Am. Chem. Soc. 1994, 116, 10336–10337. (e) Wiest, O.; Montiel, D. C.; Houk, K. N. J. Phys. Chem. A 1997, 101, 8378–8388. (f) Black, K. A.; Wilsey, S.; Houk, K. N. J. Am. Chem. Soc. 1998, 120, 5622– 5627. (g) Staroverov, V. N.; Davidson, E. R. THEOCHEM 2001, 573, 81– 89. (h) Tantillo, D. J.; Hoffmann, R. J. Org. Chem. 2002, 67, 1421–1426. (i) Jabbari, A.; Houk, K. N. Org. Lett. 2006, 8, 5975–5978. (8) (a) Wilsey, S.; Houk, K. N. J. Am. Chem. Soc. 1998, 120, 5622– 5627. (b) Navarro-Va´zquez, A.; Prall, M.; Schreiner, P. R. Org. Lett. 2004, 6, 2981–2984. (9) Brzostowska, E. M.; Hoffmann, R.; Parish, C. A. J. Am. Chem. Soc. 2007, 129, 4401–4409. (10) Frisch, M. J.; et al. Gaussian 03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (11) (a) Becke, A. D. J. Chem. Phys. 1993, 98, 1372–1377. (b) Becke, A. D. J. Chem. Phys. 1993, 98, 5648–5652. (c) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785–789. (d) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994, 98, 11623–11627. (12) Hehre, W.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. (13) Houk, K. N.; Beno, B. R.; Nendel, M.; Black, K.; Yoo, H. Y.; Wilsey, S.; Lee, J. K. THEOCHEM 1997, 398-399, 169–179. (14) Hrovat, D. A.; Beno, B. R.; Lange, H.; Yoo, H.-Y.; Houk, K. N.; Borden, W. T. J. Am. Chem. Soc. 2000, 122, 7456–7460. (15) Goldstein, E.; Beno, B.; Houk, K. N. J. Am. Chem. Soc. 1996, 118, 6036–6043. (16) (a) Dunning, T. H., Jr.; Hay, P. J. In Modern Theoretical Chemistry; Schaefer, H. F., III, Ed.; Plenum: New York, 1976; Vol. 3, p 1. (b) Fuenteabla, P.; Preuss, H.; Stoll, H.; Szentpaly, L. Chem. Phys. Lett. 1989, 89, 418. (17) Chisholm, M. H.; D’Acchioli, J. S.; Pate, B. D.; Patmore, N. J.; Dalal, N. S.; Zipse, D. J. Inorg. Chem. 2005, 44, 1061–1067. (18) Gra¨fenstein, J.; Cremer, D. Mol. Phys. 2001, 99, 981–989. (19) Gra¨fenstein, J.; Kraka, E.; Filatov, M.; Cremer, D. Int. J. Mol. Sci. 2002, 3, 360–394. (20) Yamanaka, S.; Kawakami, T.; Nagao, H.; Yamaguchi, K. Chem. Phys. Lett. 1994, 231, 25–33. (21) Yamaguchi, K.; Jensen, F.; Dorigo, A.; Houk, K. N. Chem. Phys. Lett. 1988, 149, 537–542. (22) Bauemschmitt, R.; Ahlrichs, R. J. Chem. Phys. 1996, 104, 9047– 9052. (23) Beno, B. R.; Fennen, J.; Houk, K. N.; Linder, H. J.; Hafner, K. J. Am. Chem. Soc. 1998, 120, 10490–10493.
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