The [C<sub>6</sub>H<sub>10</sub>]<sup>•+</sup> Hypersurface:  the Parent Radical Cation Diels−Alder Reaction

1999-07-03T00:00:00Z (GMT) by Matthias Hofmann Henry F. Schaefer
Various possible reaction pathways between ethene, <b>1</b>, and butadiene radical cation (<i>cis</i>-, <b>2</b>, <i>trans</i>-, <b>11</b>) have been investigated at different levels of theory up to UCCSD(T)/DZP//UMP2(fc)/DZP and with density functional theory at B3LYP/DZP. A stepwise addition involving open chain intermediates and leading to the Diels−Alder product, the cyclohexene radical cation, <b>6</b>, (path A) was found to have a total activation barrier Δ<i>G</i><sup>298≠</sup> = 6.3 kcal mol<sup>-1</sup> and a change in free Gibbs energy, Δ<i>G</i><sup>298</sup>, of −33.5 kcal mol<sup>-1</sup>. On the <i>E</i>° potential energy surface, all transition states are lower in energy than separated <b>1</b> + <b>2</b>, the exothermicity Δ<i>E</i> = −45.6 kcal mol<sup>-1</sup>. A more direct path B could be characterized as stepwise with one intermediate only at the SCF level but not at electron-correlated levels and hence might actually be a concerted strongly asynchronous addition with a very small or no activation barrier (UCCSD(T)/DZP//UHF/6-31G* gives a Δ<i>G</i><sup>298≠</sup> of 0.8 kcal mol<sup>-1</sup>). The critical step for another alternative, the cyclobutanation−vinylcyclobutane/cyclohexene rearrangement, is a 1,3-alkyl shift which involves a barrier (Δ<i>G</i><sup>298≠</sup>) only 1.7 kcal mol<sup>-1</sup> higher than that of path A for both <i>cis</i>-, <b>2</b>, (path C) and <i>trans</i>-butadiene radical cation, <b>11</b> (path D). However, from the <b>1</b> + <b>11</b> reactions, ring expansion of the vinylcyclobutane radical cation intermediate, <b>14</b>, to a methylene cyclopentane radical cation, <b>16</b>, (path E) requires an activation only 1.3 kcal mol<sup>-1</sup> larger than for path D. While cis/trans isomerization of free butadiene radical cation requires a high activation (24.9 kcal mol<sup>-1</sup>), a reaction sequence involving addition of ethene (to stepwise give an open chain intermediate <b>13</b> and vinyl cyclobutane radical cation, <b>10</b>) has a barrier of only 3.5 kcal mol<sup>-1</sup> (Δ<i>G</i><sup>298≠</sup>). This sequence also makes ethene and butadiene radical cations to exchange terminal methylene groups.