INTERMEDIATE HARDNESS DECOUPLING SCHEMES FOR CHEMICAL-REACTIVITY

Alternative charge-decoupling schemes in the two-reactant system are e xamined. They are based upon the reactive system hardness tensor in th e atoms-in-molecules (AIM) resolution, eta = partial derivative 2E/par tial derivative N partial derivative N = partial derivative mu/partial derivative N, where E is the system energy, the vectors N and mu stan d for the AIM electron populations and chemical potentials, respective ly, and the differentiation is carried out for the fixed external pote ntial due to the nuclei. Besides the familiar (totally decoupled) repr esentation of the eta eigenvectors (populational normal modes, PNM) tw o intermediate decoupling schemes am considered: internal (intra-react ant) PNM defined by the eigenvectors of the reactant diagonal blocks o f eta, and external (inter-reactant) PNM, corresponding to the transfo rmation removing the off-diagonal (coupling) block of eta. Illustrativ e results are reported for the cis-butadiene-ethylene system and for s elected adsorptions of toluene on model vanadium oxide cluster. The ha rdness coupling between the reactant internal modes is examined in som e detail. The external modes are shown to exhibit a degree of localiza tion in the AIM electron population displacements; they are naturally divided into subsets of soft and hard modes, of comparable mode hardne ss in each group, exhibiting mostly internal polarization and external charge transfer components, respectively. A possible use of these thr ee sets of populational modes in the charge sensitivity description of the two-reactant reactivity is briefly commented upon. The internal P NM representing the independent charge redistribution channels of an o pen reactant in a charge transfer process, am finally compared with th e polarizational PNM corresponding to a constant global number of elec trons.