Electronegativity according to Mulliken

See also -> electronegativity according to Pauling, -> electronegativity according to Mulliken. 

The definition of electronegativity, according to Mulliken, assumes its dependence on the valence state of atoms that allows one to reject the idea of a single EN for each atom independent of its hybridization. Thus, the necessity arises to take into account an orbital in which the valence electron is localized. 

When investigating this question, Hinze and Jaffe [3] introduced the concept of orbital electronegativity and developed a semi-empirical method to calculate the ionization potential (ly) and electron affinity, ) of any valence state. This allowed to determine electronegativity according to Mulliken s procedure taking into account the corresponding v ence states of atoms... 

Electronegativity according to Mulliken — In 1934, Robert S. MuUiken (1896-1986) [i,ii] introduced his electronegativity scale. He defined the electronegativity of an element X () ) as the average of the first ionization energy and electron affinity... 

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. 

According to Mulliken (1934, 1935), electronegativity is the algebraic mean of the first ionisation potential and of electron affinity. 

The term electronegativity (x) was initially coined by Pauling [263, 264], which virtually meant the power of an atom in a molecule to attract bonded electrons towards itself. Mulliken [265, 266] further defined the term electronegativity (/) as a function of the two main experimentally determined parameters of a system, viz., the first ionization energy (IF) and the electron affinity (EA) and showed that / may be expressed as an arithmetic mean of the respective /F and EA values. Thus, according to Mulliken ... 

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

Mulliken population analysis. This treatment shows how a molecule under investigation distributes electrons according to the atomic orbital occupancy. Note that the overlap population between two atoms is divided evenly between them without consideration of possible differences in atom types, electronegativities, and so on. 

This formula determines the sign of the dipole moment. According to the present assumptions, the sign of the adsorption dipole would be determined by the difference of the work function of the metal and the Mulliken electronegativity of the atom to be adsorbed. 

We see that the Mulliken and Pauling electronegativities seem to be reasonably in step, with electronegativity increasing from Li to C to F, in accord with experience, but with A making quintet C more electronegative than F. Evidently 7 and A act together to determine atomic avidity for electrons. 

Table 7 indicates the good agreement between these values and values of Mulliken s electronegativity, given according to equation (151) by... 

The o-components can also be obtained by calculation of all o-moments according to the approach suggested by Mulliken and Coulson [86,87], with the inclusion of homopolar and atomic dipoles and using Slater atomic orbitals [88-90]. Other possibilities are to calculate the o-electronic charges on the individual atoms [91-93] or the Del Re approach [94,95]. Some of the eariy papers devoted to dipole moments calculated by the PPP method were later subjected to a criticism by Exner [18], In one of the older studies, satisfactory dipole moments were obtained for pyridine and pyrrole using the variable electronegativity SCF method [96],... 

According to Pearson, A// can be obtained from the difference in the Mulliken electronegativity of H and the Mulliken orbital electronegativity of LjjM, as shown in Eq.3 ... 

The final atomic radii equation that has to be solved in terms of Mulliken electronegativity is authors formulation above. However, before to arrive at the effective atomic radius equation, it should be first transformed according to the forms of atomic potential and associate homogeneous density. Performing this substitutions for the main ingredients of S-DFT electronegativity expression (4.354) we get successively (Putz, 2012b,c) ... 

Electronegativities of Atoms According to the Scales of Pauling and Mulliken ... 

According to Baldwin s rules, the anionic 5-endo-trig cyclization is a disfavoured process, but it has been found to be facilitated by the introduction of two fluorine atoms at the terminal carbon atom. ° Extensive ab initio calculations (Gaussian 94 and Mulliken) for homoallylic alkoxides found that the highly electronegative fluorine atoms stabilized both transition state and product. 

The 6 -values are related to Mulliken s electronegativities X, according to Vandorffy by the equation... 

Considering the last paragraphs it is not siurprising that the important criterion for the formation of various types of bonds, that is the electronegativity, is also given by the arithmetical mean of the ionization and electron aflmity Thus, whether a molecule takes the form M+X or the form M X+ depends, according to Eq. (2.13), upon the difference (Im — Ax) — (Ix — Am), so, in fact, upon (Im + Am) — (Ix + Ax). The contribution described by Eq. (2.12c) does not enter the consideration because it is the same in each case. The equivalence of this concept by Mulliken with that of Pauling (see above) can be demonstrated by means of a simple Hiickel calculation (see, for example. Ref. [20]). 

A stable system, such as a molecule, attains a common chemical potential among its components. That is, there is no net force to transfer electron density from one point to another. The idea that chemical potential is equivalent throughout a molecule, and specifically between bonded atoms, accords with the concept of electronegativity equalization (see Section 1.1.4). Chemical potential is related to electrophilicity and nucleophilicity. A system with an attraction toward electrons is electrophilic, whereas a system that can donate electrons is nucleophilic. Chemical potential is considered to be the opposite of absolute (Mulliken) electronegativity and can be approximated by... 

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