Intermediate hardness decoupling schemes for chemical reactivity

Abstract

Alternative charge-decoupling schemes in the two-reactant system are examined. They are based upon the reactive system hardness tensor in theatoms-in-moiecules (AIM) resolution,\(\eta = \partial ^2 E/\partial N\partial N = \partial \tilde \mu /\partial N\), whereE is the system energy, the vectors N and\(\tilde \mu \) stand for the AIM electron populations and chemical potentials, respectively, and the differentiation is carried out for the fixed external potential due to the nuclei. Besides the familiar (totally decoupled) representation of the η eigenvectors (populational normal modes, PNM) two intermediate decoupling schemes are considered:internal (intra-reactant) PNM defined by the eigenvectors of the reactant diagonal blocks of η, andexternal (inter-reactant) PNM, corresponding to the transformation removing the off-diagonal (coupling) block of η. Illustrative results are reported for thecis-butadiene-ethylene system and for selected adsorptions of toluene on model vanadium oxide cluster. The hardness coupling between the reactant internal modes is examined in some detail. The external modes are shown to exhibit a degree of localization in the AIM electron population displacements; they are naturally divided into subsets ofsoft andhard modes, of comparable mode hardness in each group, exhibiting mostly internal polarization and external charge transfer components, respectively. A possible use of these three sets of populational modes in the charge sensitivity description of the two-reactant reactivity is briefly commented upon. The internal PNM representing the independent charge redistribution channels of anopen reactant in a charge transfer process, are finally compared with thepolarizational PNM corresponding to a constant global number of electrons.