On geometric concepts in sensitivity analysis of molecular charge distribution

Publisher Website
Google Scholar
Abstract
A geometric interpretation of molecular charge redistributions [polarization (P) and/or charge transfer (CT)] is proposed. It regards the atoms‐in‐a‐molecule (AIM) electron populations, N = (N1,…, Nm), as components of the global electron population vector, \documentclass{article}\pagestyle{empty}$\overrightarrow N \equiv N$ , in a system of orthogonal AIM electron population axes, \documentclass{article}\pagestyle{empty}$(\overrightarrow N _1 ,...,\overrightarrow N _m )$ . The normal (decoupled) representation corresponds to the rotated, principal axes coordinate system, \documentclass{article}\pagestyle{empty}$(\overrightarrow Q _1 ,...,\overrightarrow Q _m )$ , in which the canonical AIM hardness tensor becomes diagonal. Such transformation preserves 𝒩 while not preserving the global electron population, N = ∑miNi, the usual parameter of the sensitivity analysis. The chemical potential, hardness, softness, and related concepts associated with 𝒩 are defined and their properties examined. A simple geometric model of a chemical reaction is proposed within the \documentclass{article}\pagestyle{empty}$ \{ \overrightarrow Q _\alpha \}$ space. It consists of two intersecting effective states representing the charge activation of reactants and the charge relaxation of products, respectively. Only the normal modes of reactants, which include the CT component, can participate in the CT reaction coordinate, whereas the pure P modes contribute only to the entropy factor of the reaction rate constant. The implications of the model for the chemical reactivity are briefly explored. Finally, the linear vector space interpretation of charge sensitivities is given and applied to define the optimum hybrid charge displacement modes of reactants.