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Related Experiment Video

Updated: May 30, 2026

Quantitative Hardness Measurement by Instrumented AFM-indentation

Quantitative Hardness Measurement by Instrumented AFM-indentation

Published on: November 22, 2016

A new approach to local hardness.

T Gál¹, P Geerlings, F De Proft

¹Department of General Chemistry (Member of the QCMM Alliance Ghent-Brussels), Free University of Brussels (VUB), Pleinlaan 2, 1050 Brussel, Belgium. galt@phys.unideb.hu

Physical Chemistry Chemical Physics : PCCP

|July 28, 2011

Summary

This study introduces a novel definition for local hardness, addressing ambiguities in previous methods. The new approach provides a more accurate measure of molecular hardness and softness distribution.

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Area of Science:

Quantum Chemistry
Theoretical Chemistry
Materials Science

Background:

The conventional definition of local hardness, derived from the chemical potential's derivative, suffers from ambiguity and fails to integrate correctly.
Existing methods do not always correlate peak local hardness values with the hardest molecular regions.
Local softness, unlike local hardness, integrates to the global softness value.

Purpose of the Study:

To propose and validate a new, more robust definition of local hardness.
To develop a local hardness measure that integrates to the global hardness.
To establish a favorable local inverse relationship between the new local hardness and the Fukui function.

Main Methods:

Defining a local chemical potential from the energy density functional's derivative.
Differentiating the local chemical potential with respect to electron number to obtain local hardness.
Comparing the new local hardness definition with conventional methods using numerical tests on molecules.

Main Results:

The new local hardness definition integrates to the global hardness.
The proposed local hardness exhibits a local inverse relationship with the Fukui function.
Numerical tests on selected molecules demonstrate the efficacy of the new definition.

Conclusions:

The novel approach resolves ambiguities and limitations of previous local hardness definitions.
The new local hardness offers a reliable indicator of local softness and hardness within electron systems.
This refined understanding of local hardness has implications for predicting molecular reactivity and properties.