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Quantitative Hardness Measurement by Instrumented AFM-indentation
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Local hardness equalization: exploiting the ambiguity.

Paul W Ayers1, Robert G Parr

  • 1Department of Chemistry, McMaster University, Hamilton, Ontario, Canada. ayers@mcmaster.ca

The Journal of Chemical Physics
|June 6, 2008
PubMed
Summary
This summary is machine-generated.

The frontier local hardness offers a clear, unbiased measure in chemical reactivity, simplifying reagent design. This principle equalizes chemical potential and hardness in ground states for predictable reactivity.

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Area of Science:

  • Chemical Physics
  • Theoretical Chemistry
  • Quantum Chemistry

Background:

  • Local hardness is an ambiguous concept in density-functional theory (DFT) of chemical reactivity.
  • Existing definitions of local hardness lack clarity and consistent mathematical structure.

Purpose of the Study:

  • To critically examine three common definitions of local hardness: frontier, total, and unconstrained.
  • To elaborate on the mathematical structure underlying the ambiguity of local hardness.
  • To highlight the advantageous properties of the frontier local hardness.

Main Methods:

  • Mathematical analysis of the local hardness concept within DFT.
  • Critical examination of frontier, total, and unconstrained local hardness definitions.
  • Information-theoretic and computational analysis of the frontier local hardness.

Main Results:

  • The frontier local hardness exhibits a smaller norm and is information-theoretically unbiased compared to other definitions.
  • For ground electronic states, frontier local hardness equals global hardness.
  • The chemical potential and frontier local hardness are equalized for ground state electronic systems.

Conclusions:

  • The frontier local hardness equalization principle offers a robust computational method for designing chemical reagents.
  • This principle aids in predicting and controlling chemical reactivity profiles.
  • The study clarifies the ambiguity surrounding local hardness in DFT.