The EEM approach to chemical hardness in molecules and solids: Fundamentals and applications

Abstract

The Elcctronegativity Equalization Method (EEM), a semi-empirical approach rooted in density functional theory, enables the direct computation of the first and second order derivatives of the energy with respect to the number of electrons (N) and the external potential (v). Within this framework, various response properties of a system, as defined in the sensitivity analysis, can be evaluated. The method and its extensions are outlined, compared with other (theoretical and empirical) approaches, and applied to model systems. Applications are mainly sought in the field of structural chemistry and heterogeneous catalysis. From the theory, general rules addressing hardness/softness-structure-reactivity relationships are formulated. These provide the experimental chemist with guidelines to understand and predict the properties of materials and their role in perturbing and activating adsorbed molecules.

Electrophilic behaviour of 3-methyl-2-methylthio-1,3,4-thiadiazolium salts: A multimodal theoretical approach

“…Later, the concept of softness 17 has been found to be intimately related to fundamental variables of DFT, 18 thus providing a more solid theoretical basis to the HSAB principle, 19 and allowing one to quantify the hardness or the softness of a chemical species by using operational formulas. 20 Various applications of both global and local reactivity descriptors within this context of chemical reactivity and site selectivity have been reviewed in detail. 21 In particular, the electronic chemical potential, 22 µ, is the derivative of the energy of the molecule (or atom) with respect to its number of electrons (N) at constant external potential v(r) (i.e., identical nuclear charges and positions), and it is identified as the opposite of the electronegativity, χ (Eq.…”

Sensitivity analysis of charge transfer systems: In situ quantities, intersecting state model and its implications

“…This illustrative application identifies the critical internuclear separation of atomic reactants, at which the B -A electron jump occurs, as the distance marking the onset of the internal charge instability in the A (halogen)-B (alkali metal) system: vCT = 0. This analysis stresses the need for using the proper, biased chemical potentials and hardnesses of reactants [52], when the donor (of B) and acceptor (of A) functions of reactants are unambiguously predetermined by their chemical potentials. This illustrative case also demonstrates the adequacy of the underlying quadratic approximation in describing such subtle CT phenomena.…”

Coupling Between Electronic and Geometrical Structures

“…7.3.4), with Z i standing for the atomic number of the nucleus: (14.78) here the symbol | 0 implies that the derivative is taken for the neutral atom, when N i ¼ Z i . This quadratic (Mulliken) interpolation (e.g., Baekelandt et al 1993) of the energies of the neutral atom and its singly charged ions then expresses the two atomic derivatives in the preceding equation in terms of the atom ionization potential I i and its electron affinity A i :…”