Absolute Electronegativity and Chemical Hardness

Quantum Nanochemistry Volume II Quantum Atoms and Periodicity 

Many years after, a new emerging form of quantum mechanics, the DFT, appears as the modem quantum frame in which a chemical system (an atom, an ion, a radical, a molecule or several molecules) can be treated in a state of interaction (Parr Yang, 1989). In this modem context, the cornerstone EN definition of Parr as the minus of the chemical potential ( ) of a system in a grand canonical ensemble at zero temperature (7) was formulated (in atomic units), see (Parretal., 1978),j = -/r asinEq. (3.1), when the ground state energy E is assumed to be a smooth function of the total number of electrons N. 

Due to the Hohenberg and Kohn theorems (1964), all properties of the ground state are functions only on iVand V(r). Therefore, much chemistry is comprised in above EN, as /r = /lc[N, E(r )] measures the escaping tendency of an electronic cloud from the equilibrium system. 

However, if the finite-difterence (ED) approximation of Parr EN (3.1) is employed, around the referential integer total number of electrons the original Mulliken formula (4.3) for EN is formally recovered 

Nevertheless, at this point an opportunity for confusion and misunderstanding can arise. This because there is a conceptual difference between the DFT values of IP and EA, that are for the ground state of a system, in definition (4.247), and their averaged values on the supposed valence or excited states, as displayed in Eq. (3.1). Such dichotomy can be transposed at the potential level in the Parr picture, since V(r) is a non-zero constant the almost vertical values are involved, whereas in the Mulliken approach the almost adiabatic case is fixed by setting V r) = 0, as no further electrons are attached to the system. 

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Electron transfer is governed, in global terms, by two important parameters of atomic or molecular systems, the concepts of which have been introduced, modified, redefined, and extended from time to time. These concepts of absolute electronegativity " and chemical hardness form only a subset of the larger set of concepts that chemists have introduced over the years to understand, interpret, systematize, and rationalize chemical knowledge. 

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. 

Putz, M. V. (2010a). On absolute aromaticity within electronegativity and chemical hardness reactivity pictures. MATCH Commun. Math. Comput. Chem. 64(2), 391-418. 

Now, unfolding the AIM and MOL schemes for electronegativity and chemical hardness implementation in absolute of compactness aromaticity... 

The introduced electronegativity and chemical hardness-based absolute aromaticity formulations (4.19) and (4.20) and ordering based on their chemical reactivity principles are to be in tested next for paradigmatic molecules and other aromaticity criteria. 

The HOMA, TOPAZ, TIR, REPE, and A indices and their aromatic scales for a series of representative benzenoid hydrocarbons are presented in Table 4.10. In order to compare them with the actual electronegativity and chemical hardness-based absolute aromaticities the AIM electronegativity and chemical hardness values are first computed and reported in Table 4.10 based on Eqs. (3.252) and (3.248), respectively then, they were combined with the CFD counterparts for all schemes from Table 3.8 applied on Eqs. (3.375) and (3.376) through employing the semi-empirical AMI quantum mechanically calculation of the involved frontier orbitals and energies the resulted absolute aromaticities are presented in Tables 4.11 and 4.12, respectively. 

Table 4. Quantum chemical electronegativity and hardness indices for atoms bonded in diatomic molecules. Absolute electronegativity and hardness of molecules, calculated by the same method, is also shown. After Ref. [31]...

FIGURE 4.13 The comparative trend of tire atomic finite difference chemical electronegativity Xj, and chemical hardness from Table 4.3 (upper) with respect to the atomic absolute electronegativity zT and and hardness from Table 4.8 (middle),... 

Pearson, R. G. Absolute electronegativity, hardness, and bond energies, Bonding Energetics in Organometallic Compounds , Ed. Marks, T. J. American Chemical Society Washington, 1990, pp. 251-262. 

While the electronegativity and the absolute hardness are global properties of the system, the reaction between two molecules depends on the properties of the involved orbitals. In order to measure the chemical reactivity of a particular orbital in a molecule, different local variables, such as orbital softness (sq) and Fukui (fpolarization functions (no), can be computed through equations 24, 34, 36. 

Parr and I had originally called t] the absolute hardness. The reason was that it was a companion parameter to Xu (or —p), called the absolute electronegativity, because it had a sound basis in fundamental theory. While this made sense for ju, it seemed unnecessary for rj. The other scientific use of the term hardness would be for physical or mechanical hardness. Thus the name chemical hardness seems more appropriate for rj. 

Fig. 1.44. Correlation between empirical (Pauling) electronegativity, (Xpauiing) hardness (t)), and absolute (Mulliken) electronegativity (A abs) From R. G. Pearson, Chemical Hardness, Wiley-VCH, Weinheim, 1997, p. 54.

Putz, M. V. (2008). Absolute and Chemical Electronegativity and Hardness, Nova Publishers Inc., New York. 

Turning to the non-experimental but matter intrinsic chemical indices, in the Figure 4.13 there are represented side-by-side the atomic scales of electronegativity and of its hardness companion from the finite difference iXpj and of Table 4.3), the absolute A i and of Table VI), and... 

Putz MV (2008b) Absolute and chemical electronegativity and hardness. Nova Science, New York... 

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