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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...
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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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Related Experiment Video

Updated: Apr 25, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Average local ionization energy generalized to correlated wavefunctions.

Ilya G Ryabinkin1, Viktor N Staroverov2

  • 1Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada.

The Journal of Chemical Physics
|September 1, 2014
PubMed
Summary

This study generalizes the average local ionization energy to electron correlation methods. The new average local electron energy function is applicable to a broader range of electronic structure calculations.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • The average local ionization energy (ALIE) is a descriptor of chemical reactivity.
  • Existing ALIE definitions are limited to one-determinantal methods like Hartree-Fock and Kohn-Sham DFT.
  • This limitation restricts its application in correlated electronic structure calculations.

Purpose of the Study:

  • To generalize the ALIE function for broader applicability.
  • To develop a new descriptor for chemical reactivity applicable to correlated wavefunctions.
  • To reinterpret ALIE in terms of electron energy and density matrices.

Main Methods:

  • Reinterpreting the negative of ALIE as the average total electron energy.
  • Rewriting the quantity in terms of reduced density matrices.
  • Developing a generalized Fock operator and applying it to correlated wavefunctions.

Main Results:

  • A generalized average local electron energy (GALE) function is derived.
  • GALE naturally extends to correlated wavefunctions.
  • GALE reduces to the original ALIE for one-determinantal methods.

Conclusions:

  • The GALE function provides a unified and more broadly applicable descriptor of chemical reactivity.
  • This generalization enhances the utility of local electronic properties in computational chemistry.
  • The study bridges the gap between single-reference and multi-reference electronic structure theories.