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The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
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What can lattice DFT teach us about real-space DFT?

Nahual Sobrino1, David Jacob1,2, Stefan Kurth1,2,3

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This study connects lattice density functional theory (DFT) to real-space DFT. It shows how lattice models with specific interactions can accurately predict electronic behavior, even for molecules like hydrogen, without breaking spin symmetry.

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Area of Science:

  • Computational Chemistry
  • Condensed Matter Physics
  • Quantum Chemistry

Background:

  • Density Functional Theory (DFT) is a powerful quantum mechanical method for electronic structure calculations.
  • Lattice DFT models offer a simplified approach to complex systems, but their connection to real-space DFT is not always clear.
  • Understanding electronic behavior in molecules and materials is crucial for developing new technologies.

Purpose of the Study:

  • To establish a formal connection between lattice DFT and real-space DFT.
  • To investigate the role of specific interactions (density-density, Hund's rule, pair-hopping) in lattice DFT models.
  • To demonstrate the applicability of the developed lattice DFT model to real molecular systems, such as the hydrogen molecule.

Main Methods:

  • Utilizing Mermin's DFT formulation in the grand canonical ensemble at finite temperature.
  • Developing a two-level lattice DFT model incorporating density-density, Hund's rule, and pair-hopping interactions.
  • Applying the model to a hydrogen molecule in a minimal basis and embedding it in standard DFT calculations for larger systems.

Main Results:

  • The lattice DFT description with density-density and Hund's rule interactions is equivalent to exact-exchange in real-space DFT.
  • The inclusion of pair-hopping interaction leads to non-integer Kohn-Sham (KS) occupations, even at zero temperature.
  • The two-level lattice DFT model accurately reproduces full configuration interaction results for the hydrogen molecule, including dissociation limits and spin symmetry preservation.
  • Embedding the model into standard DFT calculations yields results in good agreement with exact calculations.

Conclusions:

  • A clear link between lattice and real-space DFT has been established.
  • The developed lattice DFT model provides an accurate and efficient method for electronic structure calculations.
  • The model's ability to handle non-integer KS occupations and preserve spin symmetry offers advantages over traditional methods.