Reactivity and polarizability response

This chapter aims to present the fundamental formal and exact relations between polarizabilities and other DFT descriptors and is organized as follows. For pedagogical reasons, we present first the polarizability responses for simple models in Section 24.2. In particular, we introduce a new concept the dipole atomic hardnesses (Equation 24.20). The relationship between polarizability and chemical reactivity is described in Section 24.3. In this section, we clarify the relationship between the different Fukui functions and the polarizabilities, we introduce new concepts as, for instance, the polarization Fukui function, and the interacting Fukui function and their corresponding hardnesses. The formulation of the local softness for a fragment in a molecule and its relation to polarization is also reviewed in detail. Generalization of the polarizability and chemical responses to an arbitrary perturbation order is summarized in Section 24.4. 

As the formation of a covalent bond between two atoms implies a (dipolar) deformation of the density, polarizability and reactivity must be related. Indeed, Nagle demonstrated an empirical relation between the atomic polarizabilities (response to a field) and the scales of electronegativities (reactivity) [36]. More... 

On both experimental and theoretical grounds there is little doubt of the importance of polarizability as a major factor in determining the commonly encountered, though variable, high RS /RO ratios. Were thermodynamic carbon affinities mainly responsible for the usual reactivity order RS > RO, the peculiar behavior of chloroquinolines would be very difficult to understand. There is some indication, however, that carbon affinities roughly parallel basicities (hydrogen affinities), In the latter case, lower RS /RO ratios could be explained in terms of the intermediate complex mechanism, ... 

NONLOCAL POLARIZABILITY AND CHEMICAL REACTIVITY 24.3.1 Potential Response Function and Fukui Functions... 

This has been developed since 1986. The title letters stand for Localized Delocalized Response. The localized effect is Charton s preferred name for the inductive effect and delocalized effect is his preferred name for the resonance effect. Indeed, he would like to change the usual symbols from <7/ to 0/, and or to op for the purposes of the Extended Hammett (EH or LD) equation109. The response referred to is that of the substituent to the electronic demand of the site (i.e. reaction site in the correlation analysis of reactivity). Thus this equation, like the PSP equation, is concerned with the parametrization of substituent polarizability. 

When one tries to rationalize the effect of the solvent on any type of chemical reactivity, considerable problems are encountered due to the multiple factors responsible for the solute/solvent interaction.2 7 One of the common ways to take into account the solvent effect is to consider it in terms of polarity (or polarizability) of the solvent. However, this concept is vague and difficult to define precisely. A first tentative... 

In contrast to oxygen and nitrogen as donor atoms, sulfur has low lying, unoccupied 3 -orbitals available. MO calculations reported in the literature, however, indicate that this influence might be overestimated. It has to be assumed that the high polarizability of the electrons on the sulfur atoms is responsible for the variety of structures and the reactivity of metal complexes with sulfur-containing ligands. 

We note that in the course of dealing with the fifth issue, the introduction of nonlocal chemical responses, we have successfully addressed the third issue, the definition of isoelectronic reactivity indices for both localized and extended systems. We note also that recognition of the need for a nonlocal description of chemical responses came early. Huckel s bond-bond polarizability [49] is in fact a simplified version of P(r, r ) [3]. 

---