Electronegativity and chemical hardness

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. 

In this way, we have concepmally surveyed how chemical reactivity in general and chemical bonding in particular may be modeled through a minimum set of electronic indices of electronegativity and chemical hardness, which are complementary in their role in promoting and stabilizing electronic strucmres in chemical combinations. 

Overall, the quantum many-body theory (i.e., the second quantizatimi of fields) and its chemical version as DFT may be regarded as the appropriate quantum tools. Quantum chemistry should be used in formulating and implementing the specific indicators of stability and reactivity, ammig which electronegativity and chemical hardness are the most preeminent and versatile. 

Table 8 The values of chemical power for the CIPAHs of Fig. 6 computed using definition (3) applied to the electronegativity and chemical hardness values from Tables 6 and 7...

Nevertheless, the other way around, it is worth recognizing that Z alone is not enough for providing further insight into the atomic chemical properties such as atomic radii, electronegativity and chemical hardness, when further account of the principal, orbital and core shielding effects count as well (see next chapters of the present volume). 

The issue of quantum observabifity of electronegativity and chemical hardness are firsdy treated such that to distinguishing among the possible occupancies they circumvent for a given quantum state under a parabolic Hamiltonian. 

Then, the associated atomie electronegativity and chemical hardness scales will be computed under general path integral quantum statistic framework and their periodic characteristics discussed respecting the general guidelines of the acceptability criteria and the finite-difierence counterparts. 

Such an application is to be in next presented for electronegativity and chemical hardness indices computations. 

FOURTH ORDER FOR SEMICLASSICAL ELECTRONEGATIVITY AND CHEMICAL HARDNESS... 

The Slater resulted values for atomic valence states, are in Table 3.1 presented, along the electronegativity and chemical hardness computed scales, respectively, in the next section. 

Eqs. (3.156)-(3.167). However, one should use the calibrated expressions for the electronegativity and chemical hardness for H atom, with the obtained pre-factors are summarized in the Table 3.2. With these the results for the elements of the first five periods of Periodic System are listed in Table 3.3. 

The main characteristic of the actual atomic scales of electronegativity and chemical hardness is that a striking difference in terms of orders of magnitudes is observed between elements down groups. 

However, this is not surprising because Ihe actual definition of electronegativity and chemical hardness reflects the holding power wifii which the whole atom attracts valence electrons to its center. There is therefore natural that as the atom is richer in core electrons down groups lesser is the attractive force on the outer electrons from the center of the atom. In this respect, the actual scales mirror at the best the atomic stability at the valence shell. 

Regarding the different orders of semiclassical influence on the electronegativity and chemical hardness values there is clear form Table 3.3 that at least fourth order expansion is necessary to achieve convergence. For this reason, in what follow only the electronegativity and chemical hardness scales based on the combinations (3.156) and (3.162) will be discussed and compared with those obtained from the finite-difference approach displayed in Table 3.1. 

TABLE 3.2 Calibration Coefficients of the Electronegativity and Chemical Hardness tf for the Considered Orders of Semiclassical Expansions (3.156)-(3.167) Such Way Their Values for Atomic H to Recover the Respective Finite Difference Ones (as given in Table 3.1) (Putz, 2007)... 

TABLE 3.3 The Electronegativity and Chemical Hardness Values of Ordinary Elements Through Employing the Components of Table 3.1 in Eqs. (3.156)-(3.167) with the Periodic Inputs (w, and of Table 3.1 and the Energetic Calibrated Pre-Factors of Table 3.2... 

After all, the present electronegativity and chemical hardness values establish new viable scales, grounded on intrinsic quantum properties of the atoms. 

The analysis of data represented in Figure 3.1 leads to three major conclusions for the use of the Green function propagators in evaluating the reactivity indices of electronegativity and chemical hardness (Putz, 2007) ... 

Putz, M. V. (2011). Electronegativity and chemical hardness different patterns in quantum chemistry. Current Physical Chemistry 1(2), 111-139 (DOI 10.2174/1877946811101020111). 

The consequences of the joint consideration of Bohmian mechanics and the golden ratio for the main atomic systems will be explored, and the quantum chemical valence state will be accordingly described alongside the so-called universal electronegativity and chemical hardness, refining the work of (Parr Bartolotti, 1982) as well as generalizing the previous Bohmian-Boeyens approach (Boeyens, 2005, 2011). 

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