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.
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.
The structural origin of hard-soft behavior in atomic acids and bases has been explored using a simple orbital model. The Pearson principle of hard and soft acids and bases has been taken to be the defining statement about hard-soft behavior and as a definition of chemical hardness. There are a number of conditions that are imposed on any candidate structure and associated property by the Pearson principle, which have been exploited. The Pearson principle itself has been used to generate a thermodynamically based scale of relative hardness and softness for acids and bases (operational chemical hardness), and a modified Slater model has been used to discern the electronic origin of hard-soft behavior. Whereas chemical hardness is a chemical property of an acid or base and the operational chemical hardness is an experimental measure of it, the absolute hardness is a physical property of an atom or molecule. A critical examination of chemical hardness, which has been based on a more rigorous application of the Pearson principle and the availability of quantitative measures of chemical hardness, suggests that the origin of hard-soft behavior for both acids and bases resides in the relaxation of the electrons not undergoing transfer during the acid-base interaction. Furthermore, the results suggest that the absolute hardness should not be taken as synonymous with chemical hardness but that the relationship is somewhat more complex. Finally, this work provides additional groundwork for a better understanding of chemical hardness that will inform the understanding of hardness in molecules.
The identification of the absolute hardness of density functional theory with chemical hardness has proven to be problematic. A rather detailed examination of absolute hardness has revealed that it is in conflict with the commonly accepted interpretation of chemical hardness. To examine chemical hardness in detail, an operational definition has been proposed that gives rise to an interpretation of chemical hardness, which is consistent with that of absolute hardness.
The electron distribution is fundamental in determining chemical and physical properties of substances. In a very qualitative fashion electronegativity is used throughout the chemistry curriculum as an indicator of atomic charge-and thus electron distribution.Because electronegativity is a far more fundamental concept than previously thought, it should be continually developed in sophistication throughout the curriculum. However, after electronegativity is introduced in the first semester of the first course (1-3) little is done to develop the concept further(4-ft>). For example, electron distributions and bonding are covered in most physical chemistry texts, yet electronegativity, which is essential to these concepts, is all but neglected.The Value of the Quantitative Approach Unfortunately, the student's understanding of electronegativity remains very qualitative, and atomic charge discussions are subject to a great deal of hand-waving. Of course
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