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The Energies of Atomic Orbitals

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Related Experiment Video

Updated: Nov 14, 2025

Photoelectron Imaging of Anions Illustrated by 310 Nm Detachment of F−

Photoelectron Imaging of Anions Illustrated by 310 Nm Detachment of F⁻

Published on: July 27, 2018

Energy natural orbitals.

Kazuo Takatsuka¹, Yasuki Arasaki¹

¹Fukui Institute for Fundamental Chemistry, Kyoto University, 606-8103 Kyoto, Japan.

The Journal of Chemical Physics

|March 9, 2021

Summary

We introduce energy natural orbitals (ENOs) to analyze complex electronic wavefunctions and electron wavepackets. ENOs offer a novel way to understand chemical reactions by tracking orbital populations during reactions.

Area of Science:

Quantum Chemistry
Theoretical Chemistry
Computational Chemistry

Background:

Analyzing highly correlated electronic wavefunctions and electron wavepackets is computationally challenging.
Existing methods struggle with extremely complex systems like quasi-degenerate excited-state manifolds.

Purpose of the Study:

To propose and demonstrate a new method for analyzing complex electronic wavefunctions and electron wavepackets.
To introduce energy natural orbitals (ENOs) as a tool for understanding chemical reactions.

Main Methods:

Numerical demonstration of energy natural orbitals (ENOs).
ENOs are defined as eigenfunctions of the energy density operator.
Analysis of electronic wavefunctions from methods like configuration interaction and cluster expansion.

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Angle-resolved Photoemission Spectroscopy At Ultra-low Temperatures

Angle-resolved Photoemission Spectroscopy At Ultra-low Temperatures

Published on: October 9, 2012

Related Experiment Videos

Last Updated: Nov 14, 2025

Photoelectron Imaging of Anions Illustrated by 310 Nm Detachment of F−

Photoelectron Imaging of Anions Illustrated by 310 Nm Detachment of F⁻

Published on: July 27, 2018

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

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

Published on: May 27, 2020

Angle-resolved Photoemission Spectroscopy At Ultra-low Temperatures

Angle-resolved Photoemission Spectroscopy At Ultra-low Temperatures

Published on: October 9, 2012

Main Results:

ENOs are one-electron functions that can represent complex electronic wavefunctions.
The sum of ENO orbital energies equals the total electronic energy.
ENO populations vary during chemical reactions while maintaining a constant total population.

Conclusions:

ENOs provide a powerful new framework for analyzing electronic wavefunctions and electron dynamics.
This method is applicable to a wide range of chemical reactions, including nonadiabatic and excited-state processes.
Case studies, including nonadiabatic electron transfer, demonstrate the utility of ENOs.