Jump to main content
Jump to site search


Revisiting the definition of local hardness and hardness kernel

Abstract

An analysis of the hardness kernel and the local hardness is performed to propose new definitions for these quantities that follow a similar pattern to the one that characterizes the quantities associated with softness, that is, we have derived new definitions for which the integral of the hardness kernel over the whole space of one of the variables leads to the local hardness, and the integral of the local hardness over the whole space leads to the global hardness. A basic aspect of the present approach is that the global hardness keeps its identity as the second derivative of the energy with respect to the number of electrons. The local hardness thus obtained depends on the first and second derivatives of the energy and the electron density with respect to the number of electrons. When these derivatives are approximated by a smooth quadratic interpolation of the energy, the expression for the local hardness reduces to the one intuitively proposed by Meneses, Tiznado, Contreras and Fuentealba. However, when one combines first directional derivatives with smooth second derivatives one finds additional terms that allow one to differentiate the local hardness for electrophilic attack from the one for nucleophilic attack. Numerical results related with electrophilic attacks on substituted pyridines, substituted benzenes and substituted ethenes are presented to show the overall performance of the new definition.

Back to tab navigation
Please wait while Download options loads

Publication details

The article was received on 31 Jan 2017, accepted on 30 Mar 2017 and first published on 31 Mar 2017


Article type: Paper
DOI: 10.1039/C7CP00691H
Citation: Phys. Chem. Chem. Phys., 2017, Accepted Manuscript
  •   Request permissions

    Revisiting the definition of local hardness and hardness kernel

    C. A. Polanco-Ramírez, M. A. Franco Perez, J. Carmona-Espindola, J. L. Gázquez and P. Ayers, Phys. Chem. Chem. Phys., 2017, Accepted Manuscript , DOI: 10.1039/C7CP00691H

Search articles by author