Density functional theory Mulliken electronegativity

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. 

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. ... 

In 1951, Robert Thomas Sanderson (1912-1989) introduced the principle of electronegativity equalization that proposes, when two or more atoms combine, the atoms adjust to the same intermediate Mulliken electronegativity (Sanderson, 1951). Density functional theory tells us that the Mulliken electronegativity is the negative of the chemical potential (Parr et al., 1978). Sanderson s principle then becomes very appealing in that it can be considered analogous to a macroscopic thermodynamic phenomenon - the equalization of chemical potential. When atoms interact, the electronegativity, or chemical potential, must equalize. 

In (4), E is the energy of any chemical system, N is the number of electrons, v is the potential given by the nuclei, / and A are the ionisation potential and electron affinity. These also define the Mulliken electronegativity, Xm-Density functional theory (DFT) is a branch of quantum mechanics that uses the electron density function, p, to describe a chemical system, rather than the more usual wave function. It had already been shown that the electron density contained all the necessary information to calculate the ground state energy and other properties. It is much easier to work with than wave functions. 

Reviews the main pictures for electronegativity, from Pauling and Mulliken to the author s analytical density functionals within the softness density functional theory with proper illustration of atomic periodicity ... 

It is obvious that for applying the present Mulliken electronegativity formula to the atomic systems it should be know at least the cone potential in which the valence electrons are evolved. Fortunately the pseudopotential theory provides such information for each atomic system starting from the Li one. It is natural to choose this way for our purpose because in this case the pseudopotential is seen as the external potential that applies to the valence electrons in agreement with the density functional picture. Then, the different electronic density formulation can be considered. 

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