Electrophilicity chemical hardness

We discussed mainly some of the possible applications of Fukui function and local softness in this chapter, and described some practical protocols one needs to follow when applying these parameters to a particular problem. We have avoided the deeper but related discussion about the theoretical development for DFT-based descriptors in recent years. Fukui function and chemical hardness can rigorously be defined through the fundamental variational principle of DFT [37,38]. In this section, we wish to briefly mention some related reactivity concepts, known as electrophilicity index (W), spin-philicity, and spin-donicity. 

Table 7. Estimated chemical hardness (j/), electronic chemical potential (ji), and electrophilicity indexes (

The electronic chemical potential /x, chemical hardness 17, and global electrophilicity 10 for the dipoles 83-86 are displayed in Table 11. Also included in Table 11 are the values of local electrophilicity and the values of the Fukui function for an electrophilic attack and for a nucleophilic attack fk at sites k for these dipoles. The two dipo-larophiles present similar electrophilicity values, 1.52 eV (14) and 1.49 eV (15) (see Table 1). According to the absolute scale of electrophilicity based on the co index,39 these compounds may be classified as strong electrophiles. 

To obtain ahieiarchy of the allied chemical principles (electronegativity, chemical hardness, electrophilicity, and chemical power) for a given pool of molecules of certain species and to check whether they are maintained across many species. 

Fig. 1 The workflow of structure-activity relationships involving conceptual and computational density functional theory through molecular frontier information (e.g., HOMO and LUMO), which are primarily employed as electronegativity (x) and chemical hardness (rf) indices and are then combined to form chemical power (x/2 y) and electrophilicity (x l2rj) reactivity measures. These values are correlated with observed biological and ecological activity (A) to provide the QSAR models (A ) to finally produce ligand progress curves (L) that provide a hierarchy of chemical reactivity principles involved in biological activity within a given DFT computational framework and species of interest...

We present the main results in Table 4.14 where the basic electronegativity and chemical hardness calculated by finite difference approximations in terms of IP and EA definitions are considered (Lackner Zweig, 1983). This is based on two positive arguments they are based on the Parr s DFT groimd state parabola method that is consistent with definition (4.234) of global electrophilicity electronegativity imder Mulliken... 

Reference electrophilicity is usually below both electronegativity and chemical hardness on which it relies, according to Eq. (4.234) ... 

The second volume details an atom s quantum stmcture, its diverse analytical predictions through reviews and an in-depth analysis of atomic periodicities, atomic radii, ionization potential, electron affinity, electronegativity and chemical hardness. Additionally, it also discusses the assessment of electrophilicity and chemical action as the prime global reactivity indices while judging chemical reactivity through associated principles ... 

As a working example, the thiocyanate ion (ACY) may react as a weak electrophilic molecule at its sulfur side and as a strong electrophilic (by reaction electrostatically controlled) by its nitrogen with the Lewis strong acids. Therefore, the electronegativity is actually locally complemented with its companion, the chemical hardness, or with the chemical softness, by the Fukui functions so providing a complete molecular picture of the chemical reactivity, i.e., of the tendency of the complex electronic systems to chemically react. 

The reactivity criteria were previously formulated when minimum electronegativity and maximum chemical hardness features for molecular stabilization against electrophilicity were considered in assessing the maximiun and minimum hierarchical tendencies for the associated absolute aromaticities, Eqs. (4.19) and (4.20), respectively. In fact, it is this criterion that needs to be validated in comparison with the consecrated ones, described below. 

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