Fukui Function Indices Research Articles

Charge sensitivities of catalytic clusters: Model ( n-Ni) and ( n-Ni)CO systems

Results of the semi-empirical charge sensitivity (CS) analysis are reported for model ( n-Ni q) clusters and R( n-Ni)CO chemisorption systems; q = 0, 1 +; 2 +; n = 9–189. One-to nine-layer clusters are investigated, and the convergence of calculated CSs with increasing n as well as the effect of various structural and electronic defects on CSs are examined. The reported CSs include both the atoms-in-molecules (AIM) and the normal (decoupled) mode hardnesses, Fukui function indices and related quantities for the global equilibrium electron distribution. The hardnesses corresponding to various partitionings of R = ( X|Y) into two (closed) complementary subsystems are also given. A new reactivity criterion for the charge-transfer (CT) processes is proposed in the normal representation: w α = (−6 N/−6 Q α)(∂ Q α/∂ N) φ α ƒ α, representing the relative αth mode contribution to the CT energy; here N is the number of electrons and Qα denotes the αth mode population. It is shown to provide the most selective index, exhibiting appreciable (positive, Σ α w α = 1) values only for a very few modes among all symmetric (S) modes participating in the CT. A less selective criterion follows from the mode Fukui function index, ƒ α, distributed throughout most of the S modes. The AIM Fukui function, ƒ i =∂ N i /∂ N i where N i is the ith AIM population, provides nonselective reactivity criterion, with comparable ƒ i values distributed among most of the constituent atoms. Finally, shapes of energetically most important normal modes and the patterns of the {ƒ i } distribution are compared for different structures of a metal cluster, and their possible implications for the catalytic activity are commented upon.

Basic concepts and illustrative applications of the sensitivity analysis of molecular charge distribution

Basic concepts of molecular charge sensitivity analysis, including the global and fragment (rigid and relaxed) hardness and softness ( Fukui function) parameters, are summarized. The resultant and regional parameters are defined, corresponding to the global and constrained (regional) equilibrium cases, respectively. Possible ways of modeling the canonical hardness and softness tensors of atoms-in-a-molecule (AIM) are discussed and the alternative representations of the chemical potential (electronegativity) equalization equations are examined. Of great interest in the chemical reactivity and catalysis are the decoupled normal representation, corresponding to the principal axes (diagonal) hardness tensor, and the partially decoupled Lanczos representation, generating a tridiagonal (Jacobi) hardness tensor. The illustrative numerical results for pyrrole and cyclopentadiene are reported. They include the resultant hardness and Fukui function parameters for both isolated molecules and protonation reactive systems. The effect of the molecular structural changes (bending of the CH bonds at α and β positions) on the resultant Fukui function indices is examined in some detail. Finally, possible applications in chemisorption and catalysis are identified and briefly commented upon.