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Related Concept Videos

The Quantum-Mechanical Model of an Atom02:45

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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In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
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Molecular Orbital Theory I

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An applied magnetic field causes loosely bound π-electrons in organic molecules to circulate, producing a local or induced diamagnetic field over a large spatial volume. As the molecules tumble in solution, the field generated by π-electrons in spherical substituents results in a zero net field. However, the net field generated by π-electrons in non-spherical substituents is not zero. The effect of this induced field depends on the orientation of the molecule with respect to B0, resulting in...
Electronic Structure of Atoms02:28

Electronic Structure of Atoms


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 numbers:  n, l, ml, and...

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Related Experiment Video

Updated: Jun 1, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

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Published on: May 27, 2020

Single electron densities: a new tool to analyze molecular wavefunctions.

Arne Lüchow1, René Petz

  • 1Institut für Physikalische Chemie, RWTH Aachen University, Aachen, Germany. luechow@rwth-aachen.de

Journal of Computational Chemistry
|June 4, 2011
PubMed
Summary

A novel method partitions electron density into single electron densities, revealing electron-electron interactions and the Fermi hole. This approach aids in understanding molecular bonding and electron correlation effects.

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Last Updated: Jun 1, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Published on: May 10, 2021

Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Electronic Structure Theory

Background:

  • Traditional methods often struggle to fully capture electron-electron interactions and the nuances of electron distribution in complex molecules.
  • Understanding the behavior of electrons, particularly their correlation and the resulting Fermi hole, is crucial for accurate chemical modeling.

Purpose of the Study:

  • To introduce a new partitioning scheme for many-electron wavefunctions into single electron densities.
  • To analyze the information contained within these single electron densities regarding electron-electron interactions and the Fermi hole.
  • To investigate the impact of electron correlation on these densities in molecular systems.

Main Methods:

  • Development of a partitioning scheme to decompose many-electron wavefunctions into single electron densities.
  • Analysis of the spatial arrangement and overlap of single electron densities.
  • Calculation and comparison of electron pair distributions derived from single electron densities.
  • Application of the method to water, ethane, and ethene molecules.
  • Investigation of electron correlation effects on single electron and pair densities for the water molecule.

Main Results:

  • The proposed scheme successfully partitions electron density, reflecting the most probable electron arrangements.
  • Single electron densities capture information on electron-electron interactions, including the Fermi hole, arising from wavefunction antisymmetry.
  • Overlapping single electron densities can be combined to form electron pair distributions, approximating qualitative electron pairs.
  • Analyses of water, ethane, and ethene demonstrate the scheme's applicability.
  • Electron correlation was found to influence both single electron and pair densities in the water molecule.

Conclusions:

  • The new partitioning scheme offers a valuable tool for analyzing electron density and electron-electron interactions in atoms and molecules.
  • This method provides insights into the nature of chemical bonding and the role of electron correlation.
  • The ability to approximate electron pair distributions has implications for models like Valence Shell Electron Pair Repulsion theory.