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Effective homogeneity of Fermi-Amaldi-containing exchange-correlation functionals.

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  • 1Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom.

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The Fermi-Amaldi functional combined with a density scaling functional accurately describes atomic exchange-correlation energies. This combination shows optimal effective homogeneity, closely mirroring energy errors for first- and second-row atoms.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Density Functional Theory

Background:

  • The Parr and Ghosh study (1995) highlighted the accuracy of specific functionals for atomic exchange-correlation energies.
  • Understanding the effective homogeneity of exchange-correlation functionals is key to improving theoretical models.

Purpose of the Study:

  • To provide insight into the success of the Parr and Ghosh functional.
  • To analyze the effective homogeneity of combined Fermi-Amaldi and density scaling functionals.
  • To evaluate the performance of these functionals for first- and second-row atoms.

Main Methods:

  • Analysis of a generalized functional combining the Fermi-Amaldi functional with a functional of degree k homogeneity.
  • Investigation of effective homogeneity under density scaling.
  • Comparison of percentage errors in effective homogeneities and exchange-correlation energies.

Main Results:

  • The Parr and Ghosh functional (k=1) demonstrates near-optimal effective homogeneity for the studied atoms.
  • Effective homogeneities are shown to be closely related to percentage errors in exchange-correlation energies.
  • The findings offer a deeper understanding of the functional's accuracy.

Conclusions:

  • The combination of Fermi-Amaldi and a degree-one homogeneous functional provides a robust description of atomic exchange-correlation energies.
  • Effective homogeneity is a crucial indicator of functional performance.
  • The study validates and extends the understanding of density scaling in quantum chemical calculations.