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The Quantum-Mechanical Model of an Atom02:45

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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum...
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Heteronuclear correlation spectroscopy is an analytical technique that investigates the coupling between different types of nuclei, often a proton and an X-nucleus, such as carbon-13 or nitrogen-15. This method is commonly used in nuclear magnetic resonance (NMR) spectroscopy to gain insights into complex chemical compounds' structural and compositional aspects. A typical heteronuclear correlation spectrum displays X-nucleus chemical shifts on one axis and a proton spectrum on the other...
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Machine learning accurate exchange and correlation functionals of the electronic density.

Sebastian Dick1,2, Marivi Fernandez-Serra3,4

  • 1Physics and Astronomy Department, Stony Brook University, Stony Brook, NY, 11794-3800, USA. sebastian.dick@stonybrook.edu.

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NeuralXC uses supervised machine learning to create accurate density functionals for electronic structure calculations. These machine-learned functionals improve accuracy and efficiency, offering a path toward universal applicability in chemistry and materials science.

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Area of Science:

  • Computational chemistry
  • Materials science
  • Machine learning applications

Background:

  • Density functional theory (DFT) is crucial for atomic-scale electronic structure studies.
  • The accuracy of Kohn-Sham DFT relies on approximations for exchange-correlation functionals.
  • Balancing accuracy and computational cost is a key challenge in DFT.

Purpose of the Study:

  • To introduce NeuralXC, a framework for developing density functionals using supervised machine learning.
  • To enhance the accuracy of existing approximate functionals while preserving computational efficiency.
  • To create transferable machine-learned functionals applicable across diverse chemical systems.

Main Methods:

  • Development of the NeuralXC framework utilizing supervised machine learning.
  • Training and optimization of machine-learned density functionals.
  • Evaluation of functional performance on molecular systems, including bond-breaking scenarios.

Main Results:

  • NeuralXC functionals learn meaningful physical information from training data, demonstrating transferability.
  • A NeuralXC functional optimized for water outperforms other methods in describing bond breaking.
  • The developed functionals achieve accuracy comparable to more computationally intensive methods.

Conclusions:

  • NeuralXC represents a significant advancement in designing accurate and efficient density functionals.
  • Machine learning offers a promising avenue for creating universal functionals for both molecules and solids.
  • This approach has the potential to accelerate electronic structure calculations in various scientific domains.