H-exchange between the primary and aromatic hydrogen atoms. These data can be explained only if a [C6H7+ C3H6] complex, hereafter called ß, is postulated (eq lb). The [C6H6 iso-C3H7+] complex, hereafter called, may be the precursor of iso-C3H7+(eq la). In this model the H-exchange can occur by reversible isomerization between protonated isopropylbenzene and the ß-complex, between- and/3-complexes, or both. First, ab initio calculations* 11 were carried out at the 6-31G**//3-21G level and led to the existence of local minima corresponding to both ß-and-complexes. All optimized structures were characterized as true minima through vibrational energy analysis at the 3-21G level. After correction for zero-point vibrational energy, the well depths are 39 kJ/mol for thecomplex and 13 kJ/mol for the/3-complex, relative to final products (values before correction are 46 and 20 kj/mol, re-spectively).

However, ab initio calculations are intractable for a complete exploration of the potential energy surface (PES) and remain approximate since electron correlation calculations are not feasible at present. In such complexes, the single most important con-tribution to electron correlation is the dispersion energy. We thus performed direct calculations of the interaction energy calculated as the sum of terms: electrostatic, polarization, dispersion, short-range repulsion, and exchange dispersion energies, according to the method developed by Claverie. 12" 14 We then determinated the most significant minima on the PES on the basis of a simulated annealing method. 15" 17