Mulliken orbital electronegativity

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 ... 

This definition may be applied not only to atoms but also to any atomic state likely to obtain its Ia and Ea values, e.g. for species with any electron configuration, or directly for atomic orbitals (orbital electronegativity). Some Mulliken orbital electronegativities are shown in Table 1.3. Electronegativities are indeed directly related with the effective nuclear charge experimented by the electron in these orbitals. 

At the outset of the Partial Equalization of Orbital Electronegativities (PEOE) method [28] is the electronegativity concept in the form of Eq. (11) presented by Mulliken, who put it on a sound theoretical basis [29]. 

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... 

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... 

The Gasteiger-Marsili approach uses the concept of the partial equalisation of orbital electronegativity. Electronegativity is a concept well known to chemists, being defined by Pauling as the power of an atom to attract electrons to itself. Mulliken subsequently defined the electronegativity of an atom A as the average of its ionisation potential and its electron affinity E ... 

FIGURE 4.17 From top to bottom, the representations of the orbital electronegativities and of the absolute chemical actions for C, N and O atoms versus the different percent contribution of s orbital (p 0%, sp 25%, sp 33%, sp 50% and s 100%) in pseudopotentials and basis set frameworks of electronic densities computation with path integral (PI), basis set (BS), and Mulliken-Jaffe (MJ) results of Table 4.13 (Putz et al., 2005,2009b). 

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

The physical meaning of our final equation is best seen on eqn 39. The term containing w is essentially the self-energy correction introduced by Mulliken in his analysis of electronegativities to account for the average repulsion of electrons occupying the same orbital. In order to get an idea of the orders of magnitude, let us apply eqn 39 to a model computation of FeCO, made to compare the ClPSl results of Berthier et al. [11] with those of a simple orbital scheme. Consider one of the two x systems of FeCO, treated under the assumption of full localization (and therefore strict cr — x separation)... 

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. 

A simple and robust quantitative MO-type approach (as opposed to density approaches) is the ubiquitous Mulliken population analysis [40]. The key concept of this easily programmed and fast method is the distribution of electrons based on occupations of atomic orbitals. The atomic populations do not, however, include electrons from the overlap populations, which are divided exactly in the middle of the bonds, regardless of the bonding type and the electronegativity. As a consequence, differences of atom types are not properly accommodated and the populations per orbital can be larger than 2, which is a violation of the Pauli principle a simple remedy for this error is a Lowdin population analysis that... 

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... 

Table 1 Atomic Electronegativity Parameters. The parameters 6° in [V], 61 and c in [V/e] are defined through eqs.(6.6 and 6.7). In the last two columns the Mulliken and Pauling electronegativity values, and P respectively, are given. For the inert gases, the electronegativity values given are those for doubly occupied orbitals.

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. 

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