Electronegativity Mulliken definition

Besides the already mentioned Fukui function, there are a couple of other commonly used concepts which can be connected with Density Functional Theory (Chapter 6). The electronic chemical potential p is given as the first derivative of the energy with respect to the number of electrons, which in a finite difference version is given as half the sum of the ionization potential and the electron affinity. Except for a difference in sign, this is exactly the Mulliken definition of electronegativity. ... 

This was justified as follows. The energy required to take an electron from a neutral atom Y to a neutral atom Z is /Y — AZt whereas the energy cost to take an electron from a neutral atom Z to a neutral atom Y is Iz — Ay. Hence, the two atoms Y and Z would have an equal propensity for attracting electrons or equal electronegativity if /Y — Az = Iz — AY, that is if IY + Ay = Iz + Az. This is consistent with the Mulliken definition, eqn (3.35), the factor 1/2 being arbitrary. As can be seen by comparing the two different scales in Fig. 3.5, the Mulliken values are approximately 2.8 times the Pauling values. 

The method of electronegativity equalization is used to fix the charges, with Mulliken definition of electronegativity. This is related by Parr [175] to the chemical potential of an electron gas, using Kohn-Sham approximation in the framework of density functional theory. Hence, electronegativity equalization corresponds to equating chemical potentials. 

The electronegativity of hydrocarbons is half the sum of the ionization potential plus the electron affinity, the Mulliken definition of the electronegativity of atoms. In the simplest approximation the electronegativity is constant and equal to the work function of graphite. This gives the relationship ... 

Equation (6) has been combined [35, 36] with the Mulliken definition of electronegativity, %, to obtain AE for the process A -+ A". In cases where only a single valence orbital is active in the processes A -> A and A - A , respectively, the corresponding valence orbital eigenvalue Sj of atom A directly measures % or the chemical potential p. In particular... 

Table 7 compares the theoretical values of the electronegativity differences using the Mulliken definition, the STS [Eq. (7)] and the ZTS-method [Eq. (14)],... 

This is true for our procedure for calculating partial atomic charges in a-bonded molecules (16). The method starts from Mulliken s definition of electronegativity, x> derived from atomic ionization potentials, IP, and electronegativities, EA (Equation 3)(17). 

E(Z, N) — E(Z, N— 1), that is from an ionization potential. Indeed it has already been seen in Section 7 that, for a neutral atom, n is in magnitude approximately half the ionization potential, for the case when the electron affinity is sufficiently small to be neglected. Mulliken s definition of electronegativity, namely... 

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... 

Equation [33] is Mulliken s definition of electronegativity, so the linear coefficient in the Taylor series is the electronegativity of the atom. Mulliken s definition is consistent with other electronegativity scales. The second-order coefficient, j J, is the hardness of the atom, For semiconductors, the hardness is half the band gap, and r] is an important property in inorganic and acid-base chemistry. " Physically, IP - EA is the energy required to transfer an electron from one atom to another atom of the same type,... 

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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