Absolute electronegativity, defined

We define two parameters the absolute electronegativity, which is approximately the same as electronegativity as Mulliken originally defined it for atoms, namely the average of the ionisation potential I and the electron affinity A (Equation 3.1). The other is called the absolute hardness, rj, which is identified with the difference in energy between the ionisation potential I and the electron affinity A (Equation 3.2). 

The absolute electronegativity is now defined by Equation 3.5, which is the negative of the slope of the E vs. N curve. This is a continuous function, which allows for nonintegral electron populations, a familiar concept in organic chemistry. The absolute hardness is then defined as the second integral of the same curve in Equation 3.6, which is therefore the curvature. 

Based on the research of Klopman, and Parr and Pearson (Klopman 1968 Parr and Pearson 1983), Pearson described the absolute hardness (ri) quantitatively as being proportional to the difference between I (ionization potential) and A (electron affinity) of the species (Pearson 1988). Absolute softness is defined as t). The absolute electronegativity (x) and the absolute hardness (Tj) are applied quantitatively to any given acid-base reaction. Table 3.10 presents x and Tj values for some representative metal ions. 

Once defined the global measure characterizing molecular systems, i.e., the absolute electronegativity, there is realized that the chemical hardness is not constant over the entire molecule. Therefore, also the local sizes can be defined, which have been called as Fukui functions by Parr and Yang (1984) ... 

First, let us go back one step to define the absolute electronegativity, X According to Mulliken, for atomic species, the... 

As defined by Mulliken [16], electronegativity is written using an expression similar to the absolute electronegativity ... 

Parr and Pearson 1301 defined a parameter 17, which they called "absolute hardness" (17 V4[IP-EA]), and calculated 17 for a variety of neutral and ionic Lewis acids and bases possessing from one to four atoms. These authors showed that the qualitative predictions of the HSAB model regarding the relative reactivities of these species toward one another may be obtained using the results from simple calculations of stabilization energies using 17 and electronegativity values. 

Parr and Pearson introduced the concept [10-13] of the absolute hardness ( y) of a species defined as half the negative rate at which its electronegativity change with a change in its electron population at constant potential ... 

Another electronegativity scale, which has versatile applications in chemistry, was defined by Mulliken [6], This electronegativity is absolute [6] in the sense that it does not depend on the molecular environment and can be directly obtained in terms of two experimentally measurable quantities, ionization potential (/) and electron affinity (A), of any atom or molecule as ... 

The first density derivative of E, the chemical potential, p (electronegativity x) of the density functional theory is given by Eq. (7). The absolute hardness, q, is defined [13]... 

Theoretical studies have offered additional perspectives on electronegativity. Parr and co-workers ° defined a quantity, fi, as the electronic chemical potential, which measures the escaping tendency of the electrons in the system. The value of is approximately the same as (I + A)/2, the Mulliken electronegativity, so the value Xm has been termed absolute electro-... 

The absolute hardness is not to be confused with the Mulliken-Jaffe definition of electronegativity, given by Equation (14.25), where the electronegativity / is defined as the average of the IE and EA (for the valence electrons). The absolute hardness and... 

Mulliken-Jaffe electronegativity x) and absolute hardness ( /) for the halide ions, defined using the frontier molecular orbital model. 

Electronegativity according to Mulliken is in fact a property of the orbitals. In theory, it is defined only for the bonding orbitals but it is difficult to differentiate between orbitals that are not equivalent. The absolute electronegavity, which is defined as a potential, is a property of the atom. 

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