Equivalence of Chemical Potential and Sandersons Electronegativity

Rather than go into detail of approximate numerical calculations of the chemical potential from various approximate forms of the density theory, for instance the Hartree-Fock-Slater equation (51), we shall focus some attention on models that have been built as a result of this recognition of the very intimate relation between the chemical potential and electronegativity. 

Now we consider the molecule in its ground state, with R fixed at its equilibrium value Re. Since the system is at equilibrium, dE=0 for an infinitesimal movement of charge dN= -dNA=dNn. Then the above equation becomes 

Sanderson, Chemical Bonds and Bond Energy , Academic Press, New York, 1971. 87 P. Politzer and H. Weinstein, J. Chem. Phys., 1979, 71, 4218. 

Following the lead of various workers,88-90 Politzer and Weinstein take as definition of the electronegativities %a = — (dEjdNA)R, nb and thus the above equation (154) is a statement that the electronegativities of the two atoms are equal at equilibrium. 

Politzer and Weinstein take this same model a little further by considering some general, fixed, separation R say. They assume the nuclei have been brought to this internuclear distance from another separation so quickly that the electrons have had no time to redistribute themselves. For this redistribution dE 0, and if it involves a charge transfer d/V= — diVA = diVu, then 

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