Mulliken valence state electronegativity

About at the same time, though published somewhat later, we were concerned with the calculation of valence state electronegativities following the original definition of Mulliken[23,24] and in turn we expressed the energy of an atom as a function of the charge q in a valence orbital, i.e. a hybrid orbital ready for bonding as... 

The problem has been resolved [69] by redefining electronegativity as the chemical potential of the valence state, calculated as the quantum potential of the valence electron, confined to its ionization sphere, i.e. x2 = h2/8mrl, expressed in eV. Whereas x corresponds to Pauling electronegativities, subject to simple periodic scaling, x2 corresponds to the Mulliken scale by the same type of operation. All of the many electronegativity scales in existence are simply related to the ionization radii, from which they ultimately derive. 

Table 5.5 APPENDIX Summary of ionization radii (r o), characteristic radii (rx), and Mulliken radii (Vm) in A units valence-state (xv) and Mulliken (xm) electronegativities in units of VeV interatomic distance (re) or its...

To allow for fluctuation of atomic electronegativities in response to the environment it has been proposed [120] that valence-state, rather than ground-state energies be used in Mulliken s formula to define orbital electronegativities. Despite common terminology, the valence state invoked here, is not the same as that of section 5.4, and refers to the improbable condition of an atom promoted to some hypothetical hybridized state. In the case of the carbon... 

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... 

R.S. MULLIKEN, A new electronegativity scale together with data on valence states and valence ionization potentials and electron affinities. J. Chem. Phys., 2, 782 (1934). 

As Mulliken pointed out, the ionisation potential and electron affinity are specific to a given valence state of an atom, and therefore the electronegativities of an atom s valence states would not be expected to be the same. This idea can be extended to the concept of orbital... 

It was accordingly suggested that (I + A)/2 be called the absolute electronegativity. Actually Mulliken had proposed that I and A should be those of a hypothetical valence state for an atom. In Eq. 9,1 and A are for ground states. Note that Eq. (9) refers to any chemical system, atom, molecule, ion or radical. 

Searching for the relation between the Mulliken valence- and Parr ground state-electronegativities, there was already proved that the former can be seen as the average of the last one (Komorowski, 1987 Putz, 2006) ... 

More, because we are interested in the Mulliken electronegativity (in order to can compare our formula with the available related values) it is significant to consider the unity normalization condition, see also Eq. (4.295), in the valence state (Putz, 2009b) ... 

The equation is valid for a given valence state. For instance, for trigonal boron compounds, a value of electronegativity can be defined for sp hybrid orbitals. Moreover, if the values of the ionization energy and electron affinity are expressed in MJ.moF , then the Mulliken electronegativity scale can be related to the Pauling scale by the relationship ... 

Kier and Hall noticed that the quantity (S -S) jn, where n is the principal quantum number and 5 is computed with Eq. (2), correlates with the Mulliken-Jaffe electronegativities [19, 20]. This correlation suggested an application of the valence delta index to the computation of the electronic state of an atom. The index (5 -5)/n defines the Kier-Hall electronegativity KHE and it is used also to define the hydrogen E-state (HE-state) index. 

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