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It has been suggested that the absolute hardness of density functional theory be identified with the chemical hardness of Pearson's principle of hard and soft acids and bases. It is unclear whether these two hardnesses are actually equivalent and if not how they are related. The problems arising from the identification of chemical hardness with absolute hardness are examined, as well as the problems associated with the evaluation of absolute hardnesses. The nature of absolute hardness is explored in some detail which has given rise to an interpretation which is in conflict with the commonly accepted interpretations of chemical hardness.

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The distinction between electronegativity as an isolated atom property and the property of an atom in a molecular environment is fundamental to the understanding and use of this quantity. A treatment similar to that performed by Klopman on the atomic Hamiltonian is applied to the molecular Hamiltonian. The treatment illustrates the strengths and weakness inherent in the practice of equalizing the isolated atom electronegativities of Mulliken and others. Two new approximate molecular parameters, totally derivable from atomic properties, are defined and examined.

The atomic charges derived from the extended electronegativity function, which includes the influence of bonding, were examined. These atomic charges were found to conform to an intuitive notion of atomic charge at the intermolecular, interatomic, and electronic levels. In addition, a new model for the core ionization energy has been developed. This new model for the core ionization energy explicitly considers the various relaxation processes, and relates the core ionization energy to the electronegativity function and the atomic charges.