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Application of Deep Learning-Based Medical Image Segmentation via Orbital Computed Tomography
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Published on: November 30, 2022

Orbital localization using fourth central moment minimization.

Ida-Marie Høyvik1, Branislav Jansik, Poul Jørgensen

  • 1qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, Aarhus 8000, Denmark.

The Journal of Chemical Physics
|December 20, 2012
PubMed
Summary
This summary is machine-generated.

We developed a novel orbital localization method using the fourth central moment. This approach enhances orbital tail decay, improving suitability for local correlation methods in quantum chemistry.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Electronic Structure Theory

Background:

  • Orbital localization is crucial for efficient quantum chemical calculations.
  • Existing localization methods may not optimally localize orbitals for all applications.
  • The rapid decay of orbital tails is desirable for local correlation methods.

Purpose of the Study:

  • To introduce a new orbital localization function based on the fourth central moment.
  • To improve the locality and tail decay of molecular orbitals.
  • To establish complementary measures for orbital locality.

Main Methods:

  • Developing a new localization function using the sum of the fourth central moments.
  • Applying a power to the fourth central moment as a penalty for less local orbitals.
  • Calculating occupied and virtual Hartree-Fock orbitals with the new method.

Main Results:

  • The proposed method with power two shows a more rapid tail decay for Hartree-Fock orbitals compared to other schemes.
  • The enhanced localization is beneficial for the application of local correlation methods.
  • Introduced standard orbital spread and fourth moment orbital spread as locality measures.

Conclusions:

  • The new fourth moment-based localization function effectively improves orbital locality.
  • The enhanced orbital tail decay makes them suitable for advanced local correlation calculations.
  • Orbital spread measures provide a comprehensive characterization of orbital locality.