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Related Concept Videos

Electron Orbital Model01:18

Electron Orbital Model

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.
The first shell is closest to the nucleus, and it has only one subshell with a single spherical orbital called the...
Atomic Orbitals02:44

Atomic Orbitals

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.
Hybridization of Atomic Orbitals I03:24

Hybridization of Atomic Orbitals I

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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Valence Bond Theory and Hybridized Orbitals

According to valence bond theory, a covalent bond results when: (1) an orbital on one atom overlaps an orbital on a second atom, and (2) the single electrons in each orbital combine to form an electron pair. The strength of a covalent bond depends on the extent of overlap of the orbitals involved. Maximum overlap is possible when the orbitals overlap on a direct line between the two nuclei.
A σ bond (single bond in a Lewis structure) is a covalent bond in which the electron density is...
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The Quantum-Mechanical Model of an Atom

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. Schrödinger...
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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Simple approximate physical orbitals for GW quasiparticle calculations.

Georgy Samsonidze1, Manish Jain, Jack Deslippe

  • 1Department of Physics, University of California, Berkeley, California 94720, USA.

Physical Review Letters
|November 24, 2011
PubMed
Summary

Generating unoccupied orbitals for large systems in density functional theory (DFT) is computationally expensive. This study introduces approximate physical orbitals to replace unoccupied DFT orbitals, enabling faster and accurate quasiparticle energy calculations.

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Area of Science:

  • Computational Chemistry
  • Quantum Mechanics
  • Materials Science

Background:

  • Calculating quasiparticle energies using GW methods requires unoccupied orbitals from density functional theory (DFT).
  • Generating these unoccupied orbitals becomes computationally prohibitive for large and complex systems.

Purpose of the Study:

  • To develop a computationally efficient method for quasiparticle energy calculations in large systems.
  • To replace the need for a full set of unoccupied DFT orbitals with accurate approximations.

Main Methods:

  • The study proposes using a combination of plane waves and localized basis DFT orbitals to construct approximate physical orbitals.
  • These approximate orbitals represent the continuum and resonant states of the system.
  • The method involves using only a minimal number of unoccupied DFT orbitals.

Main Results:

  • The proposed approach achieves accurate quasiparticle energy calculations without sacrificing precision.
  • It significantly reduces the computational cost associated with generating unoccupied orbitals.
  • An order of magnitude speedup in calculations for large systems is demonstrated.

Conclusions:

  • This novel method offers a computationally feasible pathway for accurate electronic structure calculations in large systems.
  • It overcomes the bottleneck of generating unoccupied orbitals in standard GW calculations.
  • The approach paves the way for more extensive studies of large-scale materials and molecules.