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Related Concept Videos

Atomic Orbitals02:44

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An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.
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The molecular orbital theory describes the distribution of electrons in molecules in a manner similar to the distribution of electrons in atomic orbitals. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital. Mathematically, the linear combination of atomic orbitals (LCAO) generates molecular orbitals. Combinations of in-phase atomic orbital wave functions result in regions with a high probability of electron density, while...
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Automatic differentiation for orbital-free density functional theory.

Chuin Wei Tan1, Chris J Pickard1, William C Witt1

  • 1Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom.

The Journal of Chemical Physics
|April 1, 2023
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Summary
This summary is machine-generated.

Automatic differentiation in orbital-free density functional theory (OFDFT) simplifies simulations. PROFESS-AD enables efficient calculation of material properties, accelerating research and development in computational materials science.

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Area of Science:

  • Computational Materials Science
  • Condensed Matter Physics
  • Quantum Chemistry

Background:

  • Differentiable programming and automatic differentiation (AD) streamline scientific computing.
  • Physics engines with AD offer simpler code, faster development, and reduced maintenance.
  • Fully differentiable simulations enable direct computation of experimental properties, surpassing finite difference methods.

Purpose of the Study:

  • Investigate the application of automatic differentiation within orbital-free density functional theory (OFDFT) simulations.
  • Introduce PROFESS-AD, a novel tool for OFDFT leveraging AD.
  • Enhance the development and testing of new density functionals and material properties.

Main Methods:

  • Implementation of automatic differentiation within the PROFESS framework for OFDFT.
  • Utilizing AD for direct evaluation of first-derivative properties (potentials, forces, stresses).
  • Leveraging AD for direct evaluation of higher-order derivative properties (bulk moduli, elastic constants, force constants).

Main Results:

  • PROFESS-AD automates the calculation of functional potentials, forces, and stresses.
  • Direct computation of higher-order properties like bulk moduli and elastic constants is achieved.
  • Concise implementations of property calculations are demonstrated compared to finite difference methods.

Conclusions:

  • PROFESS-AD significantly facilitates the development and testing of novel density functionals.
  • The tool offers more efficient and direct computation of material properties in OFDFT.
  • PROFESS-AD serves as a valuable prototyping tool, opening new avenues for OFDFT research.