Theoretical elucidation of the origins of substituent and strain effects on the rates of Diels-Alder reactions of 1,2,4,5-tetrazines.

The Diels-Alder reactions of seven 1,2,4,5-tetrazines with unstrained and strained alkenes and alkynes were studied with quantum mechanical calculations (M06-2X density functional theory) and analyzed with the distortion/interaction model. The higher reactivities of alkenes compared to alkynes in the Diels-Alder reactions with tetrazines arise from the differences in both interaction and distortion energies. Alkenes have HOMO energies higher than those of alkynes and therefore stronger interaction energies in inverse-electron-demand Diels-Alder reactions with tetrazines. We have also found that the energies to distort alkenes into the Diels-Alder transition-state geometries are smaller than for alkynes in these reactions. The strained dienophiles, trans-cyclooctene and cyclooctyne, are much more reactive than unstrained trans-2-butene and 2-butyne, because they are predistorted toward the Diels-Alder transition structures. The reactivities of substituted tetrazines correlate with the electron-withdrawing abilities of the substituents. Electron-withdrawing groups lower the LUMO+1 of tetrazines, resulting in stronger interactions with the HOMO of dienophiles. Moreover, electron-withdrawing substituents destabilize the tetrazines, and this leads to smaller distortion energies in the Diels-Alder transition states.