Collect. Czech. Chem. Commun. 2007, 72, 51-63

An Operational Definition of Relative Hardness

Peter Politzera,b,*, Jane S. Murrayb, Monica C. Conchaa and Ping Jina

a Department of Chemistry, University of New Orleans, New Orleans, LA 70148, U.S.A.
b Department of Chemistry, Cleveland State University, Cleveland, OH 44115, U.S.A.


After a brief review of polarizability, charge capacity and hardness, we look at some of the consequences of the requirement, in density functional theory, that the chemical potential and hardness be evaluated with the nuclear potential being held constant. The effects of this can be quite significant, one of them being that some molecules, especially closed-shell, may have zero chemical potentials. We propose that hardness be defined operationally through its inverse relationship to polarizability. Drawing upon correlations found earlier for the latter property, we present a formula for relative hardness in terms of the volume of a molecule and the average local ionization energy on its surface. The formula can also be applied to molecular components, e.g. functional groups, and we show - within the context of this approach - how their contributions combine to yield the hardness of the molecule. This involves a leveling-off effect that explains the relatively small range of hardness values obtained for a group of 33 molecules.

Keywords: Polarizability; Hardness; Charge capacity; Chemical potential; Group hardness; Density functional theory.

References: 54 live references.