Theoretical Study of the Aromatic Character of the Transition States of Allowed and Forbidden Cycloadditions

It is demonstrated that the resonance and delocalization energies defined in the theory of aromaticity can be computed using a VB Hamiltonian obtained from a CASSCF wave function. The resonance and delocalization energies of benzene and cyclobutadiene computed in this way are in good agreement with the accepted empirical estimates. An application of this procedure to the transition structure of the [2 pi(s) + 2 pi(s)] ethylene dimerization (as a prototype of a forbidden cycloaddition) and to the transition structure for the [2 pi(s) + 4 pi(s)] addition of ethylene and butadiene (as a prototype of an allowed cycloaddition) shows that the concepts of aromaticity and antiaromaticity can be used to rationalize the stability of transition states of pericyclic reactions. The delocalization energy, which accounts for the large stability of benzene, also rationalizes the low reaction barrier for the [2 pi(s) + 4 pi(s)] transition structure as well as the instability of square cyclobutadiene and the large reaction barrier for the [2 pi(s) + 2 pi(s)] transition structure. The magnitude of the delocalization energy itself has been rationalized in terms of exchange integrals K-ij and the related exchange density matrix elements P-ij. The 1,2 interactions give broadly similar stabilizing contributions in four- and six-electron systems. The small delocalization energy in four-electron systems (square cyclobutadiene and the [2 pi(s) + 2 pi(s)] transition structure) arises from the destabilizing effect of the 1,3 interactions. In contrast, the 1,4 interactions have a significant additional stabilizing effect on the delocalization energy of six-electron systems, benzene and the [2 pi(s) + 4 pi(s)] transition structure (while the effect of the destabilizing 1,3 interactions is smaller for geometric reasons).