Distortion/Interaction energy control of 1,3-dipolar cycloaddition reactivity

Computations of activation barriers and reaction energies for 1,3-dipolar cycloadditions by a high-accuracy quantum mechanical method (CBS-QB3) now reveal previously unrecognized quantitative trends in activation barriers. The distortion/interaction theory explains why (1) there is a monotonic decrease of -6 kcal/mol in the barrier height along the series oxides, imine, and ylide, for each class of 1,3-dipoles; (2) the corresponding nitrilium and azomethine betaines have almost identical cycloaddition barrier heights; (3) cycloadditions of a given 1,3-dipole with ethylene and acetylene have the same activation energies, in spite of v different reaction thermodynamics and frontier orbital gaps. There is a linear correlation between distortion energies Delta E X) and the activation barrier (Delta E + =0.75 Delta E (d)+ - 2.9 kcal/mol) that is general for substituted and unsubstituted 1,3-dipoles in these cycloadditions. The energy to distort the 1,3-dipole to the geometry favorable for interaction with the dipolarophile, that is, the transition state geometry, rather than frontier molecular orbital (FMO) interactions or reaction thermodynamics, controls reactivity. Interaction energies between the 1,3-dipole and the dipolarophile differentiate dipolarophile reactivity, and FMO interactions influence this.