CASSCF Calculations Reveal Competitive Chair (Pericyclic) and Boat

Article Cite This: J. Org. Chem. 2018, 83, 1717−1726

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CASSCF Calculations Reveal Competitive Chair (Pericyclic) and Boat (Pseudopericyclic) Transition States for the [3,3] Sigmatropic Rearrangement of Allyl Esters Henry W. Kreiman,† Mackenzie E. Batali,† Cooper S. Jamieson,† Molly A. Lyon,† and James A. Duncan* Department of Chemistry, Lewis & Clark College, Portland, Oregon 97219-7899, United States S Supporting Information *

ABSTRACT: (10,8)CASPT2/6-31G**//(10,8)CASSCF/6-31G** and CCSD(T)/cc-pVDZ//(10,8)-CASSCF/6-31G** calculations have been performed on the potential surface for the [3,3] sigmatropic allyl ester rearrangements of cis-3-penten-2-yl acetate (16) to trans-3-penten-2-yl acetate (17) and 3-buten-2-yl acetate (21) to trans-2-buten-1-yl acetate (22). The results are compared to DFT (B3LYP/6-31G**) calculations on the known 16 → 17 rearrangement that reported it to be concerted and pseudopericyclic through a boat-shaped transition structure (Birney, D. M. et al. J. Am. Chem. Soc. 2009, 131, 528−537). The CASSCF calculations, on the other hand, uncovered competitive concerted pathways for both the 16 → 17 and 21 → 22 rearrangements, though it was necessary to apply certain approximations in the former case. While one CASSCF pathway in each case involves a boatshaped transition structure, similar to the one located through DFT calculations, the other pathway involves a chair-shaped transition structure. Preference for chair or boat is shown to be method dependent. Moreover, examination of the CASSCF active-space orbitals clearly confirms that the boat-shaped transition structures are pseudopericyclic but significantly also established that the chair-shaped transition structures are clearly pericyclic. Conclusions based on these results, and regarding our understanding of pericyclic vs pseudopericyclic reactions, are proffered.

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INTRODUCTION Pericyclic reactions are among the most important of all chemical reactions.1 By definition, pericyclic transition states are composed of a cyclic array of atoms and an associated cyclic array of interacting orbitals that, strictly speaking, have no disconnections among them. Classified as sigmatropic rearrangements, electrocyclizations, cycloadditions, cheletropic, and group transfers, many pericyclic reactions2 are highly stereoselective in accordance with the Woodward−Hoffmann (W−H) rule3 that is well grounded in molecular orbital theory. The W−H rule can also predict which pericyclic reactions are likely to occur (“allowed”) or unlikely to occur (“forbidden”).3 All types of pericyclic reactions have been utilized in organic synthesis,2b−h especially in the synthesis of heterocycles2b and natural products.2c−h Eventually, though, a new class of important chemical reactions was recognized that appear on first glance to be pericyclic (since their transition states involve a cyclic array of atoms) but on closer inspection appear to have one or more disconnections in the cyclic array of interacting orbitals. These reactions, and their associated transition states, have been termed pseudopericyclic4 to reflect the fact that orbital disconnections occur when orbitals orthogonal to bonding orbitals in the reactant participate in the formation of new bonds and, as a result, are not required to obey the W−H rule. Thus, it is desirable to be able to predict in advance which reactions should be pericyclic and which pseudopericyclic, since © 2018 American Chemical Society

the former are more likely to be stereoselective and the latter may always be “allowed”. All five types of pericyclic reactions have been studied computationally with respect to possible pseudopericyclic versions.4,5 In many cases, and particularly in the electrocyclic case, the reactions appear to lack purely pseudopericyclic character. Some of these studies, which have all used density functional theory (DFT), have relied on magnetic and NBO analyses5g or tools such as electron fluctuation,5h electron localization function (ELF),5i or ellipticity of the electron density,5j However, inasmuch as the definition of pseudopericyclic reactions incorporates the notion of one or more orbital disconnections in a cyclic array of interacting orbitals (despite them being physically nonobservable), we have successfully used a localized orbital method, the active-space orbitals derived from complete active space self consistent field (CASSCF) calculations, in our study of several [3,3] sigmatropic6 and electrocyclic7 cases. The active-space orbitals included in our analyses are, at a minimum, those that would be used for a W−H analysis3 of a particular pericyclic reaction, i.e., those that involve bonds made or broken in the reaction, and thus also form the basis for the analyses of pseudopericyclic reactions where, as mentioned above, the W−H rule does not directly apply. Received: September 13, 2017 Published: January 19, 2018 1717

DOI: 10.1021/acs.joc.7b02316 J. Org. Chem. 2018, 83, 1717−1726

Article

The Journal of Organic Chemistry Scheme 1. Concerted Rearrangement of cis-Allyl Ester 16 to trans-Allyl Ester 17

Scheme 2. Pseudopericyclic Electron-Pushing Scheme for the [3,3] Sigmatropic Rearrangement of 18 Containing an Allyl Ester Moiety10,11

In the case of the [3,3] sigmatropic rearrangement of syn-7allenylnorbornene (1) to triene 2 (specifically an allenyl Cope rearrangement), our (8,8)CASSCF/6-31G* calculations6a revealed that two separate transition structures (TSs) leading to biradical intermediate 3 each involved an orbital disconnection at the center carbon of the allene moiety. This result would have qualified the rearrangement as being pseudopericyclic had the reaction been concerted; since it was not, we termed it an “augmented” Cope rearrangement. By way of contrast, the (8,8)CASSCF/6-31G* allenyl Cope rearrangement of 1,2,6-heptatriene (4) to triene 5 through biradical 6 had been shown by us to proceed through a transition structure (TS) that had no orbital disconnections.8

Nonetheless, similar (10,9)CASSCF/6-31G* calculations on compounds 10−15 showed that none of them rearranged in a purely pseudopericyclic manner nor did compounds with fourand five-membered rings replacing the three-membered ring of 9, leading us to surmise that [3,3] sigmatropic pseudopericyclic reactions are relatively rare.6c On the other hand, recent (10,9)CASSCF/6-31G* calculations located several examples of pseudopericyclic electrocyclic reactions of 1,2,4,6-heptatetraenes containing various nitrogen and oxygen heteroatoms that also involve orbital disconnections at nitrogen or oxygen lone-pair orbitals, in addition to cumulene ones.7b Presumably, this is due to the inherently more planar TSs expected for electrocyclizations, as opposed to the more likely chair and boat-shaped TSs of [3,3] sigmatropic rearrangements.

In the present CASSCF theoretical study, we turn our attention to the [3,3] sigmatropic rearrangement of allyl esters, specifically the known isomerization of cis-3-penten-2-yl acetate (16) to trans-3-penten-2-yl acetate (17) (cf. Scheme 1).5c We elected to use a 10,8 active space [i.e., to perform a (10,8)CASSCF calculation] to include, on reactant 16, one lone-pair of electrons in a hybridized orbital on the carbonyl oxygen atom and one lone-pair of electrons on the other oxygen that is involved with the π-system of the ester. By examining the fate of these two lone-pairs of electrons in the resulting TS (TS16→17) for a concerted rearrangement, we should be able to determine if the isomerization is pericyclic or pseudopericyclic. If the electron pairs persist in TS16→17, we would categorize the rearrangement as pericyclic, whereas if they are altered in any way we would characterize it as pseudopericyclic. Birney et al. have studied this 16 → 17 rearrangement with DFT using the B3LYP functional and the 6-31G** basis set and concluded that it is primarily pseudopericyclic through a “flattened boat” TS.5c,k,9 Interestingly, in this regard, the sole treatment of pseudopericyclic reactions in the popular physical organic

In addition, our (8,8)CASSCF/6-31G* calculations have shown that syn-5-propadienylbicyclo[2.1.0]penta-2-ene (7) and syn-6-propadienylbicyclo[2.1.1]hex-2-ene (8) both undergo concerted allenyl Cope rearrangements without involving any orbital disconnections.6b None of the above-mentioned hydrocarbon Cope rearrangements were found to be pseudopericyclic. However, our (10,9)CASSCF/6-31G* calculations on the [3,3] sigmatropic rearrangement of 9 showed it to be pseudopericyclic. Compound 9 not only possesses a cumulene moiety but nitrogen and oxygen heteroatoms and the pseudopericyclic TS for its rearrangement exhibits two orbital disconnections, one at the carbonyl carbon of the cumulene and the other involving the lone-pair orbital on the nitrogen atom.6c 1718


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The Journal of Organic Chemistry

S9, S11, S13, S15, S17, S19, S23, S25, and S30 in the Supporting Information were generated using MacMolPlt.15

chemistry text by Ansyln and Dougherty is relegated to a problem at the end of the chapter on pericyclic reactions10 and involves the [3,3] and [3,5] sigmatropic rearrangements of 18. Scheme 2 shows the [3,3] sigmatropic rearrangement of the allyl ester moiety in 18 that results in phenol 20 through a subsequent 1,5-H shift tautomerization of intermediate 19. The text question presupposes that the rearrangements are both pseudopericyclic by directing the student to identify the correct source of each electron-pushing arrow in order to show how the rearrangements do not fully conform to the notion of standard pericyclic reactions. The answer, in the solutions manual to the text, draws the five arrows as shown in Scheme 2,11 in which one lone-pair of electrons on each of two oxygen atoms is formally involved in the electron-pushing process. This corresponds to a pseudopericyclic reaction with two orbital disconnections; a classic pericyclic reaction would require only three electron-pushing arrows. However, it is not clear that there was any convincing evidence for such orbital disconnections in this case at the time the text was written. Recently, however, Birney has studied the rearrangement of 18 (cf. Scheme 2) both experimentally and computationally with DFT and concluded that the [3,5] sigmatropic rearrangement is favored kinetically over the [3,3] sigmatropic one and that the TSs for both rearrangements are pseudopericyclic.5k Our current study seeks to provide more convincing evidence for or against the notion of orbital disconnections in such rearrangements by evaluating the 16 → 17 allyl ester rearrangement with the CASSCF orbital method.

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RESULTS AND DISCUSSION We first report on a full (10,8)CASSCF study using the same 631G** basis set employed by Birney in the above-mentioned DFT study5c of a simplified version of the 16 → 17 rearrangement (cf. Scheme 1) that excludes Me3, namely the [3,3] sigmatropic rearrangement of 3-buten-2-yl acetate (21) to trans-2-buten-1-yl acetate (22) as shown in Scheme 3. This is Scheme 3. Concerted Rearrangement of Allyl Ester 21 to Structurally Isomeric Allyl Ester 22

because of some difficulties we encountered maintaining active spaces at higher basis sets when performing similar calculations on the 16 → 17 rearrangement. Since there appears to be negligible steric hindrance between Me3 and either Me1 or Me2 in TS16→17, a supposition subsequently borne out by the calculated structures (compare Figure 1 to Figure 4, Figure 2 to Figure 5, and Figure 3 to Figure 6 that demonstrate Me3 to occupy pseudoequatorial positions while Me1 and Me2 occupy pseudoaxial positions), we consider this a relatively minor modification. (A comprehensive, though approximate, treatment of the 16 → 17 rearrangement itself follows later in this section.) As shown in the bottom part of Table 1, the 21 → 22 rearrangement is exothermic by 0.2 kcal/mol, based on (10,8)CASPT2/6-31G**//(10,8)CASSCF/6-31G** calculations that include dynamic electron correlation. As reported for the 16 → 17 rearrangement case by Birney,5c we located a single and flattened boat-like TS (hereafter referred to as just a boat conformation) between reactant 21 and product 22 shown in Figure 1 and labeled Boat-TS21→22. As also shown in Table 1, the (10,8)CASPT2/6-31G**//(10,8)CASSCF/6-31G** activation energy (Ea) for the 21 → 22 rearrangement through this boat TS is 49.1 kcal/mol. Significantly, however, we also located a single and chairlike TS (hereafter referred to as just a chair conformation) between reactant 21 and product 22, also shown in Figure 1 and labeled Chair-TS21→22, and this alternative concerted rearrangement has a slightly lower (10,8)CASPT2/6-31G**//(10,8)CASSCF/6-31G** Ea of 47.8 kcal/mol (cf. Table 1). Thus, by this calculation, the chair TS (Chair-TS21→22) is demonstrated to be slightly more stable than the corresponding boat TS (Boat-TS21→22) by 1.3 kcal/mol, and a competitive relationship is established between the two TSs. The corresponding (10,8)CASSCF/6-31G**//(10,8)CASSCF/6-31G** energies (i.e, without any correction for dynamic electron correlation) are also included in Table 1 (fourth column) and show that Boat-TS21→22 would be favored over Chair-TS21→22 by 6.5 kcal/mol. Since it was only when correlation was included in the calculation that the chair TS had the lower energy, we also ran CCSD(T)/cc-pVDZ single-point calculations as one possible alternative to (10,8)CASPT2/631G** ones to gain some perspective. As can be seen by

COMPUTATIONAL METHODS

All stationary points were optimized at the CASSCF/6-31G** level and selected ones at the B3LYP/6-31G** level using Gaussian 09.12 All CASSCF structures were obtained using a (10,8) active space, i.e., 10 electrons in eight orbitals. The 10 electrons in the active spaces of reactants 16 and 21 and products 17 and 22 include the four πelectrons of the two double bonds, the two electrons of the Csp3−O σbond, one lone-pair of electrons in a hybridized orbital on the carbonyl oxygen atom, and one lone-pair of electrons on the other oxygen that is involved with the π-system of the ester. The active spaces of boat and chair forms of TS16→17, boat and chair forms of TS21→22, TS 23, and TS 24 are those that derive from the active spaces of the corresponding reactants and products. (All active space orbitals for reactants 16 and 21, products 17 and 22, and CASSCF-calculated TSs, including occupation numbers, are provided in the Supporting Information.) Dynamic electron correlation was included by running single-point (10,8)CASPT2/6-31G** calculations on all (10,8)CASSCF/6-31G** stationary points using Molcas 6.4 or 7.8.13 In addition, CCSD(T)/cc-pVDZ single-point calculations were run on all (10,8)CASSCF/6-31G** wave functions using Gaussian 09 for comparison. Numerical frequency calculations were performed on all optimized structures to obtain zero-point corrected energies. These calculations were also used to verify that all rearrangements proceed in a concerted manner: The single imaginary (negative) frequency for each TS was animated to confirm that the C−O bonds derived from the Csp3−O σbonds of the reactants and products were simultaneously breaking and forming, consistent with concerted reactions. In addition, intrinsic reaction coordinate (IRC) calculations were applied to nonmethylsubstituted boat TS 23, chair TS 24, and DFT-calculated boat TS 25 and are fully described in the Supporting Information (p S28). The three-dimensional structural representations in Figures 1 and 4 and on pp S4, S6, S8, S14, S16, S20, S21, S22, S24, S26, S29, and S31 in the Supporting Information were generated with GaussView 5.0.14 The molecular orbital representations (with the Contour Value routinely set to 0.055) of Figures 2, 3, 5, and 6 and on pp S3, S5, S7, 1719


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indistinguishable from the geometry of the CASSCF-calculated Boat-TS21→22 (cf. Figure 1), including the dihedral angles involving the carbon atoms of the two methyl groups. However, given that reoptimization of Chair-TS21→22 with B3LYP also results in DFT-Boat-TS21→22, it appears that DFT cannot locate Chair-TS21→22 as does CASSCF. That the 21 → Chair-TS21→22 → 22, 21 → Boat-TS21→22 → 22, and 21 → DFT-Boat-TS21→22 → 22 rearrangements are all concerted was demonstrated by animating the single imaginary frequency for each TS, as explained in the Computational Methods and supported by IRC results for the simpler (i.e., nomethyl groups) TSs 23, 24, and 25 (cf. p S28 of the Supporting Information). In Figure 1, this is demonstrated by the blue vectors that illustrate the normal mode of vibration corresponding to these frequencies. Larger sized versions of the Chair-TS21→22, Boat-TS21→22, and DFT-Boat-TS21→22 structures in Figure 1 are displayed in the Supporting Information on pages S14, S16, and S21, respectively. These larger structures are also annotated with the bond lengths for all the ring bonds and the values recorded for all the ring dihedral angles that quantitatively reinforce the chair and boat assignments for Chair-TS21→22, Boat-TS21→22, and DFT-Boat - TS21→22. We also examined the active-space molecular orbitals for the two CASSCF-derived TSs (Chair-TS21→22 and Boat-TS21→22) to see if it could be determined if each was pericyclic or pseudopericyclic. This turned out to be agreeably straightforward to do. Figure 2 shows what amounts to the net bonding

Table 1. ZPE-Corrected Relative (10,8)CASPT2/6-31G**// (10,8)CASSCF/6-31G**, CCSD(T)/cc-pVDZ// (10,8)CASSCF/6-31G**, and (10,8)CASSCF/6-31G**// (10,8)CASSCF/6-31G** Energies (kcal/mol) for the Stationary Points Calculated for the 16 → 17 and 21 → 22 Rearrangements (Schemes 1 and 3) and their Low or Imaginary (i) Numerical Frequencies (cm−1) CASPT2 rel energy (kcal/mol)

CCSD(T) rel energy (kcal/mol)

CASSCF rel energy (kcal/mol)

numerical frequency (cm−1)

16 17 ChairTS16→17a BoatTS16→17 ModBoatTS16→17b

0 −1.8 42.0

0 −1.6 43.7

0 −2.0 56.5

89.7 104.5 i764.1

45.8

44.0

51.4

i581.1

44.0

42.1

49.6

i592.9

21 22 ChairTS21→22 BoatTS21→22

0 −0.2 47.8

0 1.1 49.2

0 −0.2 60.5

136.1 111.6 i772.0

49.1

47.1

54.0

i609.5

structure

a

Optimized with one restraint. bSingle-point calculation on structure derived from Boat-TS16→17 coordinates after rotation of Me3 to same position as in DFT-Boat-TS16→17 (cf. Figure 4).

Figure 1. (10,8)CASSCF/6-31G**-calculated TSs Chair-TS21→22 and Boat-TS21→22 as well as B3LYP/6-31G**-calculated TS DFT-BoatTS21→22 for the 21 → 22 allyl ester rearrangement (cf. Scheme 3). Vectors (blue arrows) illustrate the normal mode of vibration corresponding to the single calculated imaginary frequency in each case. Red = oxygen, gray = carbon, white = hydrogen. [Asterisks mark the positions in which the corresponding TSs for the 16 → 17 rearrangement possess pseudoequatorial methyl groups (Me3) in place of hydrogen atoms (cf. Figure 4).]

Figure 2. Bonding (a, b, and c) and lone-pair (d and e) active-space orbitals (including occupation numbers) of the (10,8)CASSCF/631G**-calculated TS Chair-TS21→22 (cf. Figure 1). Lone-pair orbitals d and e are clearly not involved in bonding, making this a classically pericyclic TS. [Asterisks mark the position in which the corresponding TS Chair-TS16→17 possesses a pseudoequatorial methyl group (Me3) in place of a hydrogen atom (cf. Figure 5).]

comparing the data in the third column of Table 1 with that in the second column, the CCSD(T)/cc-pVDZ//(10,8)CASSCF/6-31G** and (10,8)CASPT2/6-31G**//(10,8)CASSCF/6-31G** energies for the 21 → 22 rearrangement are quite similar except that the energies of the chair and boat TSs are approximately transposed with the boat TS favored over the chair TS by 2.1 kcal/mol by the CCSD(T)/ccpVDZ//(10,8)CASSCF/6-31G** calculations. However, the chair and boat pathways remain competitive. [Also, the 21 → 22 rearrangement (cf. Scheme 3) is, perhaps surprisingly, shown to be endothermic by 1.1 kcal/mol.] In addition, we ran DFT optimizations at the B3LYP/631G** level starting with CASSCF-optimized coordinates for Boat-TS21→22 and Chair-TS21→22 and both calculations resulted in the DFT-Boat-TS21→22 structure shown in Figure 1. In addition, the geometry of DFT-Boat-TS21→22 is virtually

and nonbonding orbitals of Chair-TS21→22. (All active-space orbitals, that include the antibonding ones, are shown in the Supporting Information on p S15.) Orbitals d and e of Figure 2 clearly represent lone-pair orbitals on the oxygen atoms. In addition, orbital a involves a bonding match across the ring between two allyl bonding orbitals, orbital b involves a cross-ring antibonding matching of two bonding allyl orbitals, and orbital c represents a cross-ring bonding match between two nonbonding allyl orbitals. The inescapable conclusion is that Chair-TS21→22 is a classically pericyclic TS since the lonepair orbitals are clearly not involved in bonding, which is 1720


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with pseudopericyclicity. Furthermore, it seems likely that the [3,3] sigmatropic rearrangement of structure 18, as shown in Scheme 2, could be pseudopericyclic through a boat TS, pericyclic through a chair TS, or both (i.e., if competitive) and might depend upon which geometry, chair or boat, was more accessible. However, inasmuch as the previous experimental and DFT computational work was done on the 16 → 17 rearrangement (cf. Scheme 1) that involves three methyl groups,5c as opposed to the 21 → 22 rearrangement, discussed above, that involves only two of these methyl groups (Me1 and Me2), we hoped to similarly treat the 16 → 17 rearrangement with the CASSCF method. To that end, we were able to obtain (10,8)CASSCF/631G**-optimized structures and (10,8)CASPT2/6-31G**// (10,8)CASSCF/6-31G** and CCSD(T)/cc-pVDZ//(10,8)CASSCF/6-31G** energies for reactant 16 and product 17, and as shown in Table 1, these calculations determined that the 16 → 17 rearrangement is exothermic by a reasonable 1.8 or 1.6 kcal/mol, respectively. Unfortunately, however, and rather inexplicably since steric hindrance should not be an issue, the addition of Me3 to TS21→22 to build TS16→17 caused problems in maintaining proper active spaces during optimizations with acceptable basis sets (i.e., ≥ 6-31G*), despite considerable effort to maintain them. In the case of TS16→17 in the chair conformation, we could not obtain a fully optimized structure at basis sets higher than 6-31G, and in the case of TS16→17 in the boat conformation we lost the active space when trying to get an optimized structure with the likely correct conformational position for Me3 at basis sets higher than 3-21G*. Fortunately, we discovered that we could maintain the active space in the chair case with the 6-31G** basis set if we froze the distance between the carbon atoms of Me1 and Me2 at several preselected distances during the optimization. We began a search for the most optimum carbon−carbon distance by first freezing it at 3.581 Å, the value measured in the dimethyl (10,8)CASSCF/6-31G**-optimized structure Chair-TS21→22 (cf. Figure 1), and then increasing and decreasing it. In all, 14 such approximate TSs with the correct active space and single imaginary frequency were acquired, 12 of them with restricted carbon−carbon distances between 3.642 and 3.509 Å, separated equidistantly by approximately 0.012 Å. In addition, two other such structures with the much shorter distances of 3.242 and 3.121 Å were located. (See Figure S1 in the Supporting Information for plots of all 14 restricted carbon− carbon distances vs the corresponding (10,8)CASPT2/631G**//(10,8)CASSCF/6-31G** energies.) The structure with the lowest energy, resulting in a (10,8)CASPT2/6-31G**//(10,8)CASSCF/6-31G**-calculated Ea of 42.0 kcal/mol (cf. Table 1), was found with a restricted carbon−carbon distance of 3.630 Å, approximately

reinforced by the 2.00 orbital occupation numbers for the lonepair orbitals d and e. This is opposed to the supposition put forward that the [3,3] sigmatropic rearrangement of 18 (cf. Scheme 2) is definitely pseudopericyclic through the involvement of the lone-pair electrons as depicted by the electron-pushing arrows in Scheme 2.10 On the other hand, as should be clear by comparing the orbitals in Figure 2 with those in Figure 3, the Boat-TS21→22

Figure 3. Selected active-space orbitals (including occupation numbers) of the (10,8)CASSCF/6-31G**-calculated TS BoatTS21→22 (cf. Figure 1). Orbitals d and e appear to show that two of the reactant lone-pair orbitals are involved in bonding, resulting in a pseudopericyclic TS. [Asterisks mark the position in which the corresponding TS Boat-TS16→17 possesses a pseudoequatorial methyl group (Me3) in place of a hydrogen atom (cf. Figure 6).]

structure shown in Figure 3 is pseudopericyclic since none of its active space orbitals represent lone-pair orbitals such as d and e of Figure 2. Instead, orbitals d and e of Figure 3, both of which have orbital occupation numbers less than 2.00, appear to depict the original reactant lone-pairs participating in cross-ring bonding interaction. A reviewer has suggested that it is equally valid to compare the a orbitals for the chair and boat TSs, along with the b orbitals for each (cf. Figures 2 and 3). With its in-phase overlap of two allyl π-systems, orbital a for the chair TS is highly delocalized while for the boat TS it consists of a single allyl system localized primarily on the hydrocarbon moiety, though a small amount of overlap exists between this hydrocarbon πsystem and π-system of the ester moiety. In like manner, orbital b for the chair TS corresponds to the out-of-phase overlap of two allyl π-systems while for the boat TS it consists of a single allyl π-system localized on the ester moiety.16 It is particularly notable and interesting that the chair geometry is linked with pericyclicity and the boat geometry

Figure 4. (10,8)CASSCF/6-31G**-calculated TSs Chair-TS16→17, Boat-TS16→17, and Mod-Boat-TS16→17, as well as B3LYP/6-31G**-calculated TS DFT-Boat-TS16→17 for the 16 → 17 allyl ester rearrangement (cf. Scheme 1). (Distance between carbon atoms of pseudoaxial methyl groups in Chair-TS16→17 restrained to 3.63 Å during optimization.) Vectors (blue arrows) illustrate the normal mode of vibration corresponding to the single calculated imaginary frequency in each case. Red = oxygen, gray = carbon, white = hydrogen. 1721


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dimethyl case in which the (10,8)CASPT2/6-31G**//(10,8)CASSCF/6-31G**-calculated Chair-TS21→22 is also slightly favored over CASSCF-calculated Boat-TS21→22 by 1.3 kcal/mol (cf. Table 1). CCSD(T)/cc-pVDZ//(10,8)CASSCF/6-31G** calculations were also run on the three TSs for the 16 → 17 rearrangement as they were for the two TSs for the 21 → 22 rearrangement, with similar results shown in Table 1 (compare columns 2 and 3). This includes the fact that Mod-Boat-TS16→17 is slightly favored over Chair-TS16→17 (by 1.6 kcal/mol) just as BoatTS21→22 is slightly favored over Chair-TS21→22 (by 2.1 kcal/ mol). In adddition, the CCSD(T)/cc-pVDZ//(10,8)CASSCF/ 6-31G**-calculated Ea of 42.1 kcal/mol involving Mod-BoatTS16→17 compares even more favorably with the MP4(SDTQ)/ cc-pVDZ//B3LYP/6-31G**-calculated Ea of 41.6 kcal/mol associated with DFT-Boat-TS16→17 reported in ref 5c with only a 0.5 kcal/mol difference. When B3LYP/6-31G** calculations were run on the coordinates of the trimethyl CASSCF-calculated boat and chair TSs, (Boat-TS16→17 and Chair-TS16→17), the result was structures, in both cases, indistinguishable from DFT-BoatTS16→17 (cf. Figure 4), as reported in ref 5c, demonstrating again that only CASSCF calculations are able to locate the chair TS. That the CASSCF-calculated 16 → Chair-TS16→17 → 17, 16 → Boat-TS16→17 → 17, 16 → Mod-Boat-TS16→17 → 17, and 16 → DFT-Boat-TS16→17 → 17 rearrangements (cf. Scheme 1 and Figure 4) are all concerted was demonstrated by animating the single imaginary frequency for each TS, with supporting IRC evidence for nonmethyl cases (cf. p S28 in the Supporting Information), as explained above for the 21 → 22 rearrangement case. As was the case in Figure 1, this is shown in Figure 4 by the blue vectors that illustrate the normal mode of vibration corresponding to these frequencies. (Larger-sized versions of the structures in Figure 4 are displayed in the Supporting Information on pp S4, S6, S8, and S20, respectively. These larger structures are also annotated with the bond lengths for all the ring bonds and the values recorded for all the ring dihedral angles that quantitatively reinforce the chair and boat assignments.) In the manner reported above for the 21 → 22 rearrangement, we also examined the active-space orbitals for ChairTS16→17 and Boat-TS16→17, the two CASSCF-derived TSs for the 16 → 17 rearrangement. These are shown in Figures 5 and 6, and as can readily be seen by comparing Figure 2 with Figure 5 and Figure 3 with Figure 6, the orbitals are virtually identical, lending credence to the level of approximation used in our treatment of the 16 → 17 rearrangement. Thus, the 16 → 17 rearrangement is both pericyclic through a chair TS and pseudopericyclic through a boat TS based on the same arguments put forth above for the 21 → 22 rearrangement case involving only two methyl groups. As evident from Figure 1, Chair-TS21→22 has two pseudoaxial methyl groups, whereas both Boat-TS21→22 and DFT-BoatTS21→22 have one pseudoaxial and one pseudoequatorial methyl group. Similarly, Figure 4 shows that Chair-TS16→17 has two pseudoaxial and one pseudoequatorial methyl groups, whereas Boat-TS16→17, DFT-Boat-TS16→17, and Mod-BoatTS16→17 each have one pseudoaxial and two pseudoequatorial methyl groups. All other things being equal, pseudoequatorial methyl groups ought to be energy stabilizing relative to the energy destabilizing pseudoaxial ones and may have an effect on the relative stability of the chair vs boat TSs and perhaps on the

0.048 Å longer than that found in the CASSCF/6-31G**optimized dimethyl structure Chair-TS21→22 (cf. Figure 1). It is the structure that is labeled Chair-TS16→17 in Figure 4, where the pseudoaxial methyl groups (i.e., Me1 and Me2) are those whose carbon−carbon distance was restrained (at 3.630 Å) during optimization. When this distance was slightly increased by approximately 0.024 Å to 3.654 Å, the active space was lost. However, as mentioned above, the active space was maintained at the extremely shorter restricted carbon−carbon distances of 3.242 and 3.121 Å. (The active space was lost at a distance of 2.999 Å, however.) The trimethyl structure labeled Boat-TS16→17 in Figure 4 was obtained at the (10,8)CASSCF/6-31G** level without restricting any coordinates. As shown in Table 1, the (10,8)CASPT2/6-31G**//(10,8)CASSCF/6-31G**-calculated Ea involving this boat TS is 45.8 kcal/mol, or 3.8 kcal/mol higher than the corresponding energy of the Chair-TS16→17 structure (optimized with the restricted coordinate) next to it in Figure 4. The ring bond lengths and ring dihedral angles in Boat-TS16→17 are very similar to those found in the B3LYP/631G**-optimized structure labeled DFT-Boat-TS16→17 in Figure 4 obtained from the coordinates published in ref 5c. (See the Supporting Information, pp S6 and S20, for ring bond lengths and ring dihedral angles.) However, from Figure 4 it is also obvious that the conformational position of Me3 in DFTBoat-TS16→17 is distinctly different from its position in the CASSCF-optimized structure Boat-TS16→17: A C−H:C−H nearly eclipsing interaction is observed in the latter, involving a HCCH dihedral angle of 12.031°. By comparison, DFT-BoatTS16→17 has one HCCH dihedral angle, involving the carbon atom of Me3, of 174.475°. Rotation of Me3 in Boat-TS16→17 to give a 174.475° dihedral angle and reoptimization at the (10,8)CASSCF-level with the 3-21G* basis set gave a structure similar to DFT-Boat-TS16→17. However, with the 6-31G, 631G*, and 6-31G** basis sets the active space was unfortunately lost. Therefore, as a way to at least partially correct the structure Boat-TS16→17 for its likely improper conformation involving Me3, its Me3 was rotated to give one dihedral angle of 174.475° and a single-point (10,8)CASSCF/6-31G** calculation run on the resulting structure. This gave the modified structure labeled Mod-Boat-TS16→17 in Figure 4, and as can be seen from Table 1, it has an associated (10,8)CASPT2/6-31G**//(10,8)CASSCF/6-31G**-calculated Ea of 44.0 kcal/mol, a reasonable 1.8 kcal/mol lower than that for Boat-TS16→17 with its nearly eclipsing C−H:C−H interaction. Despite the approximations employed, this (10,8)CASPT2/6-31G**//(10,8)CASSCF/631G**-calculated Ea of 44.0 kcal/mol involving Mod-BoatTS16→17 compares favorably with the MP4(SDTQ)/ccpVDZ//B3LYP/6-31G**-calculated Ea of 41.6 kcal/mol for DFT-Boat-TS16→17 reported in ref 5c (2.4 kcal/mol difference),17 though both calculation methods (CASPT2// CASSCF and B3LYP) give higher activation energies than the experimental one (Ea = 38.6 kcal/mol) for the 16 → 17 rearrangement. Even the (10,8)CASPT2/6-31G**//(10,8)CASSCF/6-31G**-calculated Ea involving the lower energy chair TS (Chair-TS16→17) is higher than the experimental one at 42.0 kcal/mol (cf. Table 1). Most importantly, however, the (10,8)CASPT2/6-31G**//(10,8)CASSCF/6-31G**-calculated Chair-TS16→17 is 2.0 kcal/mol (cf. Table 1) more stable than the (10,8)CASPT2/6-31G**//(10,8)CASSCF/6-31G**calculated Mod-Boat-TS16→17 and suggests that the chair and boat TSs are competitive as they were found to be in the 1722


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S28), and supported through animation of their single imaginary frequencies. The calculated (10,8)CASPT2/6-31G**//(10,8)CASSCF/ 6-31G** energy difference between TSs 23 and 24 is 2.4 kcal/ mol, in favor of 24, the chair conformation, compared with the corresponding 1.3 kcal/mol energy difference calculated between Boat-TS21→22 and Chair-TS21→22, also favoring the chair conformation (cf. Table 1). Hence, the pseudoaxial vs pseudoequatorial positions of the methyl groups in BoatTS21→22 and Chair-TS21→22 appear to have relatively little influence on the conformational preferences of these TSs. There is even more agreement between the 2.4 kcal/mol energy difference between TSs 23 and 24 and the corresponding (10,8)CASPT2/6-31G**//(10,8)CASSCF/631G**-calculated 2.0 kcal/mol energy difference between Mod-Boat-TS16→17 and Chair-TS16→17. CCSD(T)/cc-pVDZ//(10,8)CASSCF/6-31G** energies were also calculated for the no-methyl TSs 23 and 24. As was the case for the other TSs for which this CCSDF(T)-level of calculation was applied (i.e., those found in Table 1), the boat TS (23) is favored over the chair TS (24), but by only 1.0 kcal/mol; whereas, as mentioned above, the (10,8)CASPT2/631G**//(10,8)CASSCF/6-31G** calculation gave an energy difference of 2.4 kcal/mol in favor of the chair TS. Moreover, when two methyl groups are “added” to both TS 23 and TS 24, to give Boat-TS21→22 and Chair-TS21→22, the CCSD(T)/ccpVDZ//(10,8)CASSCF/6-31G** energy difference between the two TSs increases by 1.1 kcal/mol but identically decreases by 1.1 kcal/mol when calculated using (10,8)CASPT2/631G**//(10,8)CASSCF/6-31G**. This appears to be consistent with there being more steric hindrance between the two methyl groups in Chair-TS21→22 than in Boat-TS21→22. This is reasonable because the two methyl groups occupy pseudoaaxial positions in the chair conformation but one pseudoaxial and one pseudoequatorial position in the boat conformation. Finally, the “addition” of the third methyl group to the dimethyl cases, to obtain Chair-TS16→17 and Mod-BoatTS16→17, results in an increase in the energy difference between them (by 0.7 kcal/mol) with CASPT2//CASSCF and a concomitant decrease in the energy difference (by 0.5 kcal/ mol) with CCSD(T)//CASSCF. It appears that introducing the third methyl group causes slightly more steric hindrance in the boat conformation than in the chair conformation. (This is at least consistent with the fact that the distance between the “third” Me carbon atom and the carbon atom of the Me in the ester moiety is 4.70 Å in Mod-Boat-TS16→17 and 4.86 Å in Chair-TS16→17.) In addition, we reoptimized the (10,8)CASSCF/6-31G**optimized boat TS 23 at the B3LYP/6-31G** level. Not

Figure 5. Bonding (a, b, and c) and lone-pair (d and e) active-space orbitals (including occupation numbers) of the (10,8)CASSCF/631G**-calculated TS Chair-TS16→17 (cf. Figure 4). Lone-pair orbitals d and e are clearly not involved in bonding making this a classically pericyclic TS.

Figure 6. Selected active-space orbitals (including occupation numbers) of the (10,8)CASSCF/6-31G**-calculated TS BoatTS16→17 (cf. Figure 4). Orbitals d and e appear to show that two of the reactant lone-pair orbitals are involved in bonding resulting in a pseudopericyclic TS.

simultaneous occurrence of both chair and boat TSs in the first place. To investigate this notion, we replaced the two methyl groups of both Boat-TS21→22 and Chair-TS21→22 with hydrogen atoms and optimized the resulting structures at the (10,8)CASSCF/6-31G** level. This led to TSs 23 and 24, respectively, shown in Figure 7 and definitively demonstrated to be TSs for concerted [3,3] sigmatropic rearrangements by IRC calculations, as described in the Supporting Information (p

Figure 7. B3LYP/6-31G** reoptimization of both (10,8)CASSCF/6-31G**-optimized boat TS 23 and (10,8)CASSCF/6-31G**-optimized chair TS 24 lead to the same boat TS 25. Vectors (blue arrows) illustrate the normal mode of vibration corresponding to the single calculated imaginary frequency in each case. Red = oxygen, gray = carbon, white = hydrogen. 1723


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We chose to vary the C1−O−O-C4 dihedral angle where C1 refers to the carbon atom between the two oxygen atoms and C4 to the carbon atom directly across the ring from C1. Initially we varied this dihedral angle, that preserves the Cs symmetry, in 5° increments, beginning with 130° (TS 24 has a C1−O−O− C4 dihedral angle of 124.09°) until the active space, which consisted entirely of orbitals corresponding to the chair conformation (cf., p S25 of the Supporting Information), was irretrivably lost at 150°. We also successfully calculated constrained TSs corresponding to dihedral angles of 146° and 147° which also preserved this active space. (The active space was lost at a dihedral angle of 148°, however.) These six points are plotted among the first seven of 14 points in Figure S2, along with the point for optimized TS 24 containing no constraints.18 We also established that the active space corresponding to the boat conformation first materialized at a C1−O−O−C4 dihedral angle of 166° with a ZPE-corrected (10,8)CASSCF/6-31G**//(10,8)CASSCF/6-31G** energy 0.9 kcal/mol below that for optimized TS 24. It is plotted along with five additional points having C1−O−O−C4 dihedral angles ranging from 170° to 210° (equivalent to −150°), separated by 10° increments (cf. Figure S2), all of which exhibited active spaces coresponding to the boat conformation (cf. p S23 of the Supporting Information). The point for optimized boat TS 23 with no constraints (C1−O− O−C4 dihedral angle of 215.25°) is also included in Figure S2. (All 12 dihedral angle constrained TSs plotted in Figure S2 were demonstrated to have only one imaginary numerical frequency as do the unconstrained TSs 23 and 24, of course.) The plot’s highest point, corresponding to a dihedral angle of 147°, is 1.2 kcal/mol above that for TS 24. The fact that this energy difference represents 31% of the energy difference between unconstrained TSs 23 and 24 is probably consistent with chair TS 24 being reasonably robust, though the activespace orbitals corresponding to the boat conformation were found to exist over a wider range of dihedral angles (3.0 kcal/ mol vs 1.2 kcal/mol for the chair conformation).

surprisingly, this resulted in the corresponding boat TS 25, as shown in Figure 7, with very similar ring bond lengths and ring dihedral angles as in TS 23. However, the identical boat TS 25 was also obtained when chair TS 24 was reoptimized using B3LYP/6-31G** (cf. Figure 7), demonstrating that even in this simplified no-methyl case that DFT does not locate a chair TS. (Larger 23, 24, and 25 structures, annotated with ring bond lengths and ring dihedral angles, are found in the Supporting Information on pages S22, S24, and S26, respectively.) In addition, the active space MOs for the (10,8)CASSCF-631G**-optimized structure 24 closely resemble the active space MOs for Chair-TS21→22 in Figure 2 and Chair-TS16→17 in Figure 5 and demonstrate that the chair form TS 24 is classically pericyclic. Likewise, the active-space MOs for the (10,8)CASSCF-6-31G**-optimized structure 23 closely resemble the active-space MOs for Boat-TS21→22 in Figure 3 and Boat-TS16→17 in Figure 5 and demonstrate that the boat form TS 23 is pseudopericyclic. (The active-space MOs for TS 23 and TS 24 are found in the Supporting Information.) Since the choice of active space is crucial to the success of CASSCF calculations, we sought to run a (14,10)CASSCF/631G** calculation on chair TS 24, i.e., one that includes all four lone-pairs of electrons, for comparison with the (10,8)CASSCF/6-31G** calculations we used throughout this study that involve two lone-pairs, to see if our results would be affected. While we were unable to locate a clean (14,10) active space, we were able to locate a clean (12,9) active space that corresponds to the inclusion of three of the four lone-pairs. As shown on p S30 of the Supporting Information, the (12,9)CASSCF/6-31G** calculation located a relatively clean set of nine active space orbitals, eight of which (all but the center one) were virtually identical to the eight active space orbitals obtained from the comparable (10,8)CASSCF/631G** calculation, including nearly identical orbital occupation numbers (cf. p S25 of the Supporting Information). The ninth (center) orbital, shown on p S30 of the Supporting Information, represents one of the sought-after extra two lone-pair orbitals (the out-of-phase one) with an approximately sp3-hybridized lobe on each oxygen atom, oriented as expected relative to the orientation of the lone-pair lobes of the other two lone-pair orbitals shown on either side of it on page S30. Notably, it also has the proper orbital occupation number of 2.00, and the optimized geometry of the (12,9) structure (cf., p S29), including dihedral angles, is nearly identical to the optimized geometry of the (10,8) stucture (cf., p S24) (Supporting Information). A corresponding (14,10)CASSCF/ 6-31G** calculation yielded the tenth orbital as an approximation to the in-phase partner of this out-of-phase ninth orbital, however it was contaminated with a significant contribution from nearby nearly in-plane nonactive-space σorbitals. Given that neither the (12,9) nor the (14,10) calculations altered the original (10,8) active space orbitals, we feel confident that our selection of a (10,8) active space was appropriate for all the rest of our CASSCF calculations. Finally, given that only the (10,8)CASSCF/6-31G** calculations, and none of the B3LYP/6-31G** calculations, locate chair TSs, be it Chair-TS16→17, Chair-TS21→22, or TS 24, one reviewer suggested we test the robustness of TS 24, the simplist case, by calculating a series of structures beginning with it but with dihedral angles forced incrementally toward a boat geometry at the (10,8)CASSCF/6-31G**//(10.8)CASSCF/631G** level. At this computational level, boat TS 23 is favored over chair TS 24 by 3.9 kcal/mol with ZPE correction.

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SUMMARY AND CONCLUSIONS The known [3,3] sigmatropic (Cope-type) rearrangement of trimethyl-substituted allyl ester 16 (cf. Scheme 1) was thoroughly studied computationally at the (10,8)CASPT2/631G**//(10,8)CASSCF/6-31G** and CCSD(T)/cc-pVDZ// (10,8)CASSCF/6-31G** levels of theory, and the results were compared to those obtained from similar calculations performed by others on the rearrangement of 16 at the B3LYP/6-31G** level and to an experimental result.5c Because of certain difficulties encountered in maintaining active spaces at higher basis sets, which required the use of certain approximations, the rearrangement of the slightly simpler dimethyl-substituted allyl ester 21 (cf. Scheme 3) was also studied at the same levels of theory. The key results obtained from these CASSCF treatments of the 16 → 17 and 21 → 22 rearrangements were very similar, despite the limitations imposed by the approximations used in the former. Each rearrangement was found to proceed in a concerted manner through both chair and boat TSs, even though the B3LYP/631G**-level study of the 16 → 17 rearrangement located only a boat TS.19 The chair TSs are slightly favored using CASPT2 to include correlation while the boat TSs are slightly favored using CCSD(T). Moreover, the active space orbitals for ChairTS16→17 and Chair-TS21→22 revealed them to be pericyclic TSs (cf. Figures 2 and 3), whereas the active space orbitals for Boat1724


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TS16→17 reasonable, but we have located corresponding chair and classically pericyclic TSs Chair-TS21→22 and Chair-TS16→17 with competitive Ea values, running somewhat counter to the more usual circumstance that pseudopericyclic TSs have lower activation barriers. Our results are also consistent with the notion that pseudopericyclic TSs tend to be more planar than pericyclic ones.20 It should be clear from inspection of the structures in Figures 1 and 4 that flattened boat and pseudopericyclic TSs Boat-TS21→22, Mod-Boat-TS16→17, and 23 are more planar than the corresponding chair and pericyclic TSs Chair-TS21→22, Chair-TS16→17, and 24. What is it, however, that links the chair TSs to pericyclicity and the boat TSs to pseudopericyclicity? Perhaps it is that the lone-pairs of electrons are more readily accessible for use in bonding in the more planar boat TSs that helps to stabilize these lone-pairs. Nevertheless, competitive chair TSs are observed too. While the lone-pairs are not so stabilized in the pericyclic chair TSs, perhaps a counterbalancing factor in their favor is the extended delocalization of the remaining six electrons (“aromaticity”), absent from the pseudopericyclic TSs as a consequence of the orbital disconnections. In any case, it is likely that a similar CASSCF study on both the [3,3] and [3,5] sigmatropic rearrangements of 18, studied recently with DFT by Birney,5k would shed additional light on this possible linkage of pericyclicity with chair TS conformations and pseudopericyclicity with boat TS conformations, at least in systems such as these.22

TS16→17 and Boat-TS21→22 revealed them to be pseudopericyclic TSs (cf. Figures 5 and 6). In addition, we found that the two methyl groups in ChairTS21→22 and Boat-TS21→22 (cf. Figure 1) have a relatively small effect on the (10,8)CASPT2/6-31G**//(10,8)CASSCF/631G**-calculated 1.3 kcal/mol and CCSD(T)/6-31G**// (10,8)CASSCF/6-31G**-calculated 2.1 kcal/mol energy differences between them (cf. Table 1). This is because we obtained corresponding energy differences of 2.4 and 1.0 kcal/mol respectively between chair TS 24 and boat TS 23 that were created by successfully optimizing the structures obtained through replacing the two methyl groups in both ChairTS21→22 and Boat-TS21→22 with hydrogen atoms (cf. Figure 7). To our knowledge, this is the first study to locate competing pericyclic and pseudopericyclic TSs in the same rearrangement, which has the potential advantage of contributing unique and fundamental insights into the general factors responsible for one rearrangement pathway being favored over the other. In this regard, it is especially notable that of the two classic transition state conformations for Cope-type rearrangements, one (the chair conformation) is clearly linked to pericyclicity and the other (the boat conformation) is clearly linked to pseudopericyclicity, based on scrutiny of the active-space orbitals unique to the CASSCF method. It has been suggested that pseudopericyclic reactions tend to have relatively planar transition states and lower activation barriers than typical pericyclic reactions.20 For example, we calculated a (10,8)CASSCF/6-31G*-level Ea of 19.4 kcal/mol for the [3,3] sigmatropic rearrangement of 9 that we demonstrated to be pseudopericyclic, while we similarly calculated Ea values of 26.2 and 22.8 kcal/mol, respectively, for the comparable rearrangements of 10 and 11 that we demonstrated to be classically pericyclic. Moreover, we calculated vanishingly small activation barriers of 1.5 and 0.1 kcal/mol, at the (12,10)CASPT2/6-31G*//(12,10)CASSCF/ 6-31G* level, for the pseudopericyclic electrocyclic ring closures of HNCH−CHCH−CHCO and O CH−CHCH−CHCO, respectively.7b,21 Somewhat higher Ea values of 13.8 and 13.9 kcal/mol were similarly calculated for the pseudopericyclic electrocyclizations of O CH−CHCH−CHCNH and HNCH−CHCH− CHCO. By sharp comparison, however, much higher Ea values of 20.5 and 20.6 kcal/mol, respectively, were similarly calculated for the electrocyclizations of HNCH−CHCHNCCH2 and OCH−CHCH-NCCH2 that we showed were classically pericyclic.7b However, there are certainly examples of much higher calculated activation barriers for perceived pseudopericyclic reactions. Most relevant to the current study is the MP4(SDTQ)/cc-pVDZ//B3LYP/6-31G**-calculated Ea of 41.6 kcal/mol for DFT-Boat-TS16→17 reported by Birney in ref 5c, promoted as being pseudopericyclica value that compares reasonably well with our (10,8)CASPT2/6-31G**//(10,8)CASSCF/6-31G**-calculated Ea of 44.0 kcal/mol and even better with our CCSD(T)/cc-pVDZ//(10,8)CASSCF/631G**-calculated Ea of 42.1 kcal/mol for Mod-Boat-TS16→17 (cf. Table 1). Birney also characterized the [3,3] and [3,5] sigmatropic rearrangements of 18 (cf. Scheme 2) as pseudopericyclic and calculated Ea values at the CCSD(T)/631G**//B3LYP/6-31G** + ZPVE level of 40.6 and 39.0 kcal/ mol, respectively.5k Hence, not only are our relatively high Ea values involving boat and pseudopericyclic TSs Boat-TS21→22 and Mod-Boat-

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.joc.7b02316. Complete ref 11. (10,8)CASSCF/6-31G** active-space MOs, and optimized geometries for 16, 17, 21−24, Boat-TS16→17, Chair-TS21→22, and Boat-TS21→22, including imaginary frequency normal mode vectors, ring bond lengths, and ring dihedral angles for the five TSs. (10,8)CASSCF/6-31G** active-space MOs and partially optimized geometries for Chair-TS16→17 and Mod-BoatTS16→17, including imaginary frequency normal mode vectors, ring bond lengths, and ring dihedral angles. B3LYP/6-31G** optimized geometries for DFT-BoatTS16→17, DFT-Boat-TS21→22, and 25, including imaginary frequency normal mode vectors, ring bond lengths, and ring dihedral angles. Uncorrected (10,8)CASSCF/631G** and ZPE-corrected (10,8)CASSCF/6-31G**, (12,9)CASSCF/6-31G**, (10,8)CASPT2/6-31G**, CCSD(T)/cc-pVDZ, and B3LYP/6-31G** energies; plots of relative energy vs Me1−Me2 carbon−carbon bond lengths for Chair-TS16→17 (Figure S1); details of IRC calculations on TSs 23, 24, and 25; plot of relative energy vs dihedral angles for constrained TSs of 24 (Figure S2) (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

James A. Duncan: 0000-0001-5754-3338 Notes

The authors declare no competing financial interest. 1725


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The Journal of Organic Chemistry †

(13) Molcas 6.4 and Molcas 7.8: Karlström, G.; Lindh, R.; Malmqvist, P.-Å.; Roos, B. O.; Ryde, U.; Veryazov, V.; Widmark, P.-O.; Cossi, M.; Schimmelpfennig, B.; Neogrady, P.; Seijo, L. Comput. Mater. Sci. 2003, 28, 222−239. Duncan, J. A. Molcas software review. J. Am. Chem. Soc. 2009, 131, 2416. (14) GaussView, Version 5: Dennington, R.; Keith, Todd; Millam, J. Semichem, Inc., Shawnee Mission, KS, 2009. (15) Bode, B. M.; Gordon, M. S. J. Mol. Graphics Modell. 1998, 16, 133−138. (16) The reviewer speculates that the CASSCF method might be biased in favor of the delocalized orbitals a and b of the chair conformation (cf. Figures 2 and 5) and that optimization using yet another level of theory might not lead to a chair TS at all, as is the case with B3LYP. (17) The MP2(SDTQ)/cc-pVDZ//B3LYP/6-31G** activation energy for DFT-Boat-TS16→17 of 44.4 kcal/mol5c is even closer to the (10,8)CASPT2/6-31G**//(10,8)CASSCF/6-31G** Ea of 44.0 kcal/mol. (18) The point corresponding to the dihedral angle of 146° is slightly lower in energy than that corresponding to dihedral angle 145° due, inexplicably, to an unusually small ZPE correction (cf. Figure S2, Supporting Information). (19) This is not the first time we have encountered major discrepancies between DFT results and our own CASSCF results: See: Duncan, J. A.; Spong, M. C. J. Phys. Org. Chem. 2005, 18, 462− 467 and refs 7a and 7b within. In addition, more recent unpublished results that examine higher-level (“Minnesota”) functionals, are also shown to be inconsistent with such CASSCF results. It should be noted, however, that we have not tested functionals beyond B3LYP on the allyl ester rearrangements reported in this article to see if they might give different TSs (e.g., chair in addition to or in place of boat ones). (20) See ref 5k and references cited therein, especially refs 4a−j. (21) When dynamic electron correlation was included by performing (12,10)CASPT2/6-31G*//(12,10)CASSCF/6-31G* calculations instead of just (12,10)CASSCF/6-31G*//(12,10)CASSCF/6-31G* ones, these Ea values actually turned negative! (22) A CASSCF study of the [3,5] sigmatropic rearrangement of 18 should be interesting for an additional reason as well. The orbital symmetry “allowed” formal pericyclic process according to the Woodward−Hoffmann rule parlance is σ2s + π2s + π4a, one that has a good chance of being undermined geometrically, due to the framework distortion that is likely necessary to accommodate the antafacial component (i.e., likely “forbidden”). Consequently, given that the [3,5] sigmatropic rearrangement has been observed to occur (and is even favored over the corresponding [3,3] sigmatropic rearrangement kinetically), it is likely pseudopericyclic (as opposed to pericyclic) as asserted by Birney et al. in ref 5k and based, in part, on DFT calculations. However, it would be desirable to determine if CASSCF calculations can indeed confirm or alternatively contradict this assertion.

Lewis & Clark College undergraduate students at the time this work was carried out.

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ACKNOWLEDGMENTS Support for this work from the John S. Rogers Science Research Program of Lewis & Clark College is appreciated. We thank Dr. David Hrovat of the University of North Texas for his extremely helpful advice in performing calculations over the past 22 years.

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REFERENCES

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