Limitations in using the Sanderson's principle to estimate global reactivity

The Sanderson's geometric mean equalization principle for electronegativity has allowedexpressions for chemical potential and molecular hardness to be derived withinthe framework of the Conceptual Density Functional Theory for obtaining molecularelectronic properties of an entire molecule or supramolecule from the isolated fragments.Along with the determination of electronic properties, in former articles it hasbeen demonstrated that Sanderson's scheme can be very useful as a method for rationalizingchemical reactions when both N (the number of electrons) and υ(r) (theexternal potential) change.The main problem that arises when using this approximationto estimate molecular properties is that the bonding potential and redistributionof the electron density among the fragments are not considered, and structural relaxationdue to new specific through-bond and through-space interactions is not allowedwithin this scheme. Therefore this principle presents an important restriction to beused. In this chapter a suitable example to expose this limitation is mathematicallydeveloped by means of a general deduced mathematical expression for a polymericgrowing chain according to this principle. This reveals that a task for improving thisscheme is pending.