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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 mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
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In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are also observed. The attractive and repulsive forces are dependent on the distance between the particles, as well as the sign and magnitude of the charges on the individual particles. When the charges on the particles are opposite, they attract each other. If both particles have the same charge, they repel each other.
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Orbitals are the areas outside of the atomic nucleus where electrons are most likely to reside. They are characterized by different energy levels, shapes, and three-dimensional orientations. The location of electrons is described most generally by a shell or principal energy level, then by a subshell within each shell, and finally, by individual orbitals found within the subshells.
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Population analysis with Wannier orbitals.

Sudipta Kundu1, Satadeep Bhattacharjee2, Seung-Cheol Lee2

  • 1Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India.

The Journal of Chemical Physics
|March 16, 2021
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Summary
This summary is machine-generated.

We developed new methods, Wannier orbital overlap and Hamilton populations, to analyze electron distribution and bonding. These techniques offer precise insights into electronic structure and interactions in various materials.

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Area of Science:

  • Solid-state physics
  • Quantum chemistry
  • Materials science

Background:

  • Traditional methods like crystal orbital overlap population (COOP) and crystal orbital Hamilton population (COHP) offer insights into chemical bonding.
  • Analyzing electron distribution and interactions within materials is crucial for understanding their properties.
  • Bridging non-local and localized electronic structure descriptions remains a challenge.

Purpose of the Study:

  • To introduce novel methods, Wannier orbital overlap population and Wannier orbital Hamilton population, for quantifying orbital contributions to electron distribution and bonding.
  • To establish a formalism that connects plane-wave density functional theory (DFT) calculations to localized Wannier orbital bases.
  • To demonstrate the utility of these methods for analyzing bonding and electron localization in diverse materials.

Main Methods:

  • Formulation of Wannier orbital overlap population and Wannier orbital Hamilton population.
  • Projection of plane-wave DFT wave functions onto a localized Wannier orbital basis.
  • Application of the formalism to analyze electron distribution and bonding in five distinct materials.

Main Results:

  • The proposed methods accurately describe the contribution of different orbitals to electron distribution and interactions.
  • The developed formalism successfully bridges non-local plane-wave bases with localized Wannier orbital bases.
  • A key advantage is a strictly zero spilling factor for insulators and systematically small values for metals.

Conclusions:

  • Wannier orbital overlap and Hamilton populations provide valuable insights into electronic structure and chemical bonding.
  • The method offers a robust way to analyze electron distribution and localization from plane-wave DFT calculations.
  • This approach enhances the understanding of bonding characteristics across various material types.