Electronegativity and Chemical Potential

N) — E(Z, N— 1), that is from an ionization potential. Indeed it has already been seen in Section 7 that, for a neutral atom, n is in magnitude approximately half the ionization potential, for the case when the electron affinity is sufficiently small to be neglected. Mulliken s definition of electronegativity, namely 

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These are constant numbers obtained from experiments or independent calculations. They are properties of the atom or the molecule and have been useful in predicting the chemical behavior of the system. In addition to its use as a scale of electronegativity, the chemical potential is also a measure of the intrinsic strength of generalized acids and bases [12]. 

It is observed that when the field is applied toward the central atom (say from the line joining the two H atoms to the O atom along the principal axis, in case of H20) of all the species, and if the central atom is more electronegative, the chemical potential and hardness decrease with increasing field values [41], For example, when the electric field is applied toward the O atom in H20, the chemical potential and hardness decrease. On the other hand, when the field is applied along the principal axis toward the central atom, the nucleophilicity decreases for that atom, provided the central atom is more electronegative. The nucleophilicity of O in H20 decreases when the electric field is applied toward that atom. Moreover, the electrophilicity of H atoms in H20 decreases. This trend is the same as observed in case of linear molecules. Here, the results of only one molecule (H20) are presented. For details, the reader may refer to our recent paper [41],... 

STRUTINSKY S SHELL-CORRECTION METHOD IN THE EXTENDED KOHN-SHAM SCHEME APPLICATION TO THE IONIZATION POTENTIAL, ELECTRON AFFINITY, ELECTRONEGATIVITY AND CHEMICAL HARDNESS OF ATOMS... 

In the next section we shall recall the definitions of the chemical concepts relevant to this paper in the framework of DFT. In Section 3 we briefly review Strutinsky s averaging procedure and its formulation in the extended Kohn-Sham (EKS) scheme. The following section is devoted to the presentation and discussion of our results for the residual, shell-structure part of the ionization potential, electron affinity, electronegativity, and chemical hardness for the series of atoms from B to Ca. The last section will present some conclusions. 

The vertex properties encoded in the column vectors p and r can be either topological, for example, vertex degree, vertex distance degree, or chemical, for example, atomic number, electronegativity, and ionization potential. 

Table 1 Synopsis of the basic principles of reactivity at the chemical potential (or electronegativity) and chemical force (or hardness) levels, with both equalization and inequality stages on valence states of atomic, pro-molecule, and atoms-in-molecule systems...

Since the introduction of the electronegativity as chemical potential with changed sign is considered to be a fundamental observable for the characterization of the equilibrium states of the electronic systems in interaction, the chemical reactivity description in terms of quantum statistics and algebraic theory is considered to be a fundamental step in elucidating the tendencies of evolution to and from the equilibrium states, admitted by an electronic system (finite) and also of the afferent critical states. 

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 ... 

Table 1.2 The Butadiene tc-system, with AN=N =4, frontier energetic quantities, ionization potential IP), electron affinity EA), electronegativity (x), and chemical hardness (rj) of Eqs. 1.7 and 1.8 - in electron volts (eV), and the resulted parabolic energy of Eq. 1.98, alongside with the 7t-related energy based on the Hiickel simplified (with Coulomb integrals set to zero, a = 0) expression of (1.97) for the experimental/Hiickel method and on the related energy form of Eq. 1.101 and the other semi-empirical methods CNDO, INDO, MINDO, MNDO, AMI, PM3, ZINDO) as described in the previous section - expressed in kilocalories per mol (kcal/mol) their ratio in the last column reflects the value of the actual departure of the electronegativity and chemical hardness parabolic effect from the pi-bonding energy, while for the first (Exp Hiickel) line it expresses the resonance contribution (and a sort of P factor integral) in (1.97) for the tt-bond in this system the eV to kcal/mol conversion follows the rule 1 eV = 23.069 kcal/mol...

However, the Hohenbeig-Kohn theorems give new conceptual quantum tools for physico-chemical characterization of an electronic sample by means of electronic density and its functionals, the total energy and chemical potential (electronegativity). Such density functional premises are in next analyzed towards elucidating of the quantum nature of the chemical bond as driven by chemical reactivity (Putz, 2007b). 

Although successful, the HSAB principle initially lacked a satisfactory quantitative basis. However, it is now possible to use DPT theory to derive electronic chemical potential values (electronic chemical potential, p, is the negative of absolute electronegativity) and chemical hardness values, These results complement the use of DFT theory to predict stability constants as described earlier in this chapter. 

Worth noting that the ionization potential and the electronic affinity can be accordingly expressed in terms of orbital electronegativity and chemical hardness functions... 

TABLE 3.10 The Hartree-Fock, B3LYP, SVWN, and BP86/6-31G Electronegativity and Chemical Hardness Computations for the HjO Molecule By Using Orbital Energies and Vertical Total Energies for Ionization Potential and Electron Affinity Calculatiorr, Respectively lRHT=intemaUy resolved hardness tensor, H/L=HOMO/LUMO (Putz et al 2004)... 

For the analytical procedure, the chemical bonding may be described by field potential relating electronegativity and chemical hardness (Putz, 2008d)... 

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