Sanderson’s principle

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. 

Engl. TransL), 296, 440 (1987). Scheme for the Calculation of the Electronegativities of Atoms in a Molecule in the Framework of Sanderson s Principle. 

An independent method of calculating ionic radii [177] uses Sanderson s principle of equalization of atomic electronegativities (see Sect. 2.4.5), it shows the metal... 

There is clear now that the Sanderson s principle of regional electronegativities equalization takes place when the transfer potentials cancel each other or, in other words, when the zero minimum difference between regional electronegativities, within the bond, is achieved ... 

Zeolites are composed of various atoms of different electronegativity (refer to Table 2.8). However, their intermediate electronegativity (i.e., geometric mean of the component atoms after redistribution of the electrons in the compound) is reported to be established as demonstrated hy Sanderson s principle of electronegativity equalization (i.e., when two or more atoms initially different in electronegativity combine chemically, they become adjusted to flie same electronegativity within the compound). The intermediate electronegativity can be determined for a compound, Qv, by Eq. (2.1) [59] ... 

The partial charges model [2], based on Sanderson s principle [3] of electronegativity equalization jn a compound, does not allow an absolutely accurate estimation of the charges, and in this respect has limitations similar to other methods. However, it is interesting to study its application to some problems of... 

These descriptors have been widely used for the past 25 years to study chemical reactivity, i.e., the propensity of atoms, molecules, surfaces to interact with one or more reaction partners with formation or rupture of one or more covalent bonds. Kinetic and/or thermodynamic aspects, depending on the (not always obvious and even not univoque) choice of the descriptors were hereby considered. In these studies, the reactivity descriptors were used as such or within the context of some principles of which Sanderson s electronegativity equalization principle [16], Pearson s hard and soft acids and bases (HSAB) principle [17], and the maximum hardness principle [17,18] are the three best known and popular examples. 

The crudest one is Sanderson s electronegativity equalization principle [39, 40] according to which atoms-in-molecule make electron transfers from lower to higher electronegative parts thus achieving equilibrium in electronegativity. 

Just like Sanderson s electronegativity equalization principle, the Hard and Soft Acids and Bases principle was originally introduced without strong theoretical basis. Nevertheless, it was used widely from its formulation on. The principle states that hard acids prefer to coordinate with hard bases and soft acids with soft bases [82], In 1983, Parr and Pearson provided a definition for the chemical hardness [25]... 

It is commonplace among chemists to think of a molecule as formed from its constituent atoms and accordingly to try to relate molecular properties to respective atomie properties. For example, Sanderson s electronegativity equalization principle (EEP) states that molecular electronegativity (chemical poten-... 

FIGURE 3.3 Sanderson s electronegativity equalization principle. (Adapted from P. Geerlings and F. De ProfL Chemical Reactivity as Described by Quantum Chemical Methods. Int. J. Mol. Sci. 3, no. 4 (2002) 276-309.)... 

In 2 computational aspects are discussed, with the assessment of DFT methods ( 2.1) in the evaluation of (a) ionization energies and electron affinities, and via eqn. (11), finite difference estimates of electronegativities and hardnesses ( 2.1.1) Mid (b) of dipole and quadrupole moments ( 2.1.2).In the final paragraph 2.2 a problem at the borderline between computational and conceptual DFT is tackled the evaluation of Fukui fimctions "beyond" the finite difference approximation. In 3 conceptual DFT is discussed, where in 3.1 attention is paid to the evaluation and/or use of DFT based concepts as such the shape factor and the local softness as Molecular Similarity indicators ( 3.1.1), and the nuclear Fukui function ( 3.1.2). In the final part of this Section ( 3.2) the role of DFT based concepts in various principles is discussed. The influence of solvent on the acidity of alkylalcohols is discussed within the framework of Sanderson s Electron ativity Equalization Principle [30] ( 3.2.1). The Hard and Soft Acids and Bases Principle and Pearson s Maximum Hardness Principle [31] are used as the guiding prindples in the study of the cycloaddition reactions of HNC to alkenes and aligmes. 

Datta, D. Geometric Mean Principle for Hardness Eualization A Corollary of Sanderson s Geometric Mean Principle of Electronegativity Equalization. J. Phys. Chem., 1986,90,4216-4217. 

Besides Pauling s electronegativity scale, estimated on the basis of the energies of bond rupture, there exist some other electronegativity scales based on various assumptions. Among these, the scales obtained by Mulliken, Allred and Rochow and Sanderson, should be mentioned. All these scales, together with the principles of their construction and the values of the electronegativities, can be found in handbooks. 

Fig. 12a, b. Evaluation of basicity by XPS and IR of adsorbed pyrrole correlation between the partial charge on N as derived from the Sanderson electronegativity equalization principle and the (a) N Is BE and (b) wavenumber of the NH vibration. Taken from HuzmgM.Adnot A, Kaliaguine S (1992) J Am Chem Soc 114 10005, with kind permission from the American Chemical Society... 

Sanderson has applied this principle indiscriminately, assuming EC to equalize for all atoms even in such species as K2SO4, where K and S play quite different chemical roles and have different valences. Later it was suggested [474, 475] to equalize EC in separate bonded pairs of atoms, rather than throughout the entire molecule. It was also observed that total equalization in organic molecules would give different EC for isomers of the same composition, and a novel, rather efficient, method of calculating EC for isomers was proposed instead [451-453]. 

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