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Chemical hardness: Temperature dependent definitions and reactivity principles.

Ramón Alain Miranda-Quintana1, Marco Franco-Pérez2, José L Gázquez2

  • 1Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4L8, Canada.

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Summary

This study demonstrates that electronic, thermodynamic, and Helmholtz hardnesses, derived from temperature-dependent density functional theory, support the hard and soft acids and bases (HSAB) and maximum hardness (MH) principles at all temperatures.

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Area of Science:

  • Quantum Chemistry
  • Theoretical Chemistry
  • Chemical Physics

Background:

  • The hard and soft acids and bases (HSAB) principle and the maximum hardness (MH) principle are fundamental concepts in chemistry.
  • Current justifications for these principles often rely on energy interpolation, which can be arbitrary.
  • A rigorous, mathematically sound foundation for these principles is needed, especially across varying temperatures.

Purpose of the Study:

  • To investigate three distinct definitions of chemical hardness within temperature-dependent density functional theory (TD-DFT).
  • To establish a mathematically robust justification for the HSAB and MH principles.
  • To determine the validity of these principles at any relevant temperature.

Main Methods:

  • Utilizing temperature-dependent density functional theory (TD-DFT) to define chemical hardness.
  • Identifying electronic, thermodynamic, and Helmholtz hardnesses as the second derivative of a thermodynamic state function.
  • Analyzing the relationship between these hardness definitions and the HSAB and MH principles.

Main Results:

  • The three chemical hardness definitions inherently imply both the HSAB and MH principles.
  • This approach provides a more mathematically sound justification compared to energy interpolation methods.
  • The HSAB and MH principles are shown to hold true at any temperature of chemical relevance, not just in the low-temperature limit.

Conclusions:

  • The TD-DFT framework offers a rigorous foundation for the HSAB and MH principles.
  • Chemical hardness, defined as a second derivative, consistently supports these fundamental chemical rules.
  • The validity of the HSAB and MH principles is extended to all temperatures, enhancing their applicability in chemical studies.