Electronegativity equalization Mulliken

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. 

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. 

This is the simplest expression for charge (ionicity) in the Mulliken-Jaffd system with electronegativity equalization (see Eq. 5.85). The boundary lines in Fig. 7.6 radiate more or less from the origin with the slope of m from Eq. 7.1. We may thus infer that each represents a line of constant ionicity that is responsible for the changeover from one structure type to the next. 

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... 

Momany s idea has led to a new definition of atomic charges. It would be possible to write volumes about atomic charges (AC), a concept that has no a precise definition in QM formalism, but is of extreme utility in practical applications. Many definitions of AC are based on manipulations of the molecular wave function, as, for example, the famous Mulliken charges. Other definitions are based on different analyses of the QM definition of the charge density, as for example Bader s charges.There are also charges derived from other theoretical approaches, such as the electronegativity equalization, or from experimental values, such as from the vibrational polar tensors. 

Atomic charges may be also derived, with simple computational techniques, by applying electronegativity equalization procedures. There are several variants of the method [126-131]. A discussion of its theoretical justification may be found in a review by Bergmann and Hinze [132]. The approach is flexible enough to allow further improvements in the parameters in our opinion, instead of aiming at a better correlation with Mulliken charges, a redefinition of the parameters based on a... 

Keywords Hartree-Fock method Kohn-Sham method Mulliken population analysis Electronegativity equalization method Atomic charges... 

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]. 

An example of quantum mechanical schemes is the oldest and most widely used Mulliken population analysis [1], which simply divides the part of the electron density localized between two atoms, the overlap population that identifies a bond, equally between the two atoms of a bond. Alternatively, empirical methods to allocate atomic charges to directly bonded atoms in a reasonable way use appropriate rules which combine the atomic electronegativities with experimental structural information on the bonds linking the atoms of interest. A widely used approach included in many programs is the Gasteiger-Hiickel scheme [1]. 

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. 

Through Mulliken s identification of dUldq as the electronegativity, we see that minimizing the energy with respect to the charges is equivalent to equalizing the electronegativities,... 

Mulliken gave an alternative definition of electronegativity in terms of the ionization energy / and electron affinity A of an atom. The ionization energy equals AE for the reaction X —> X+ + e, while the electron affinity equals AE for X -> X + e. To a rough approximation,... 

---