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Atomic Orbitals

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.

Molecular Orbital Theory I

Molecular Orbital Theory I

Overview of Molecular Orbital Theory

Electron Orbital Model

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...

Molecular Orbital Theory II

Molecular Orbital Theory II

Molecular Orbital Energy Diagrams

MO Theory and Covalent Bonding

MO Theory and Covalent Bonding

The molecular orbital theory describes the distribution of electrons in molecules in a manner similar to the distribution of electrons in atomic orbitals. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital. Mathematically, the linear combination of atomic orbitals (LCAO) generates molecular orbitals. Combinations of in-phase atomic orbital wave functions result in regions with a high probability of electron density, while...

The Energies of Atomic Orbitals

The Energies of Atomic Orbitals

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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Related Experiment Video

Updated: Dec 10, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

From orbitals to observables and back.

Anna I Krylov¹

¹Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, USA.

The Journal of Chemical Physics

|September 3, 2020

Summary

This summary is machine-generated.

This study explores Dyson orbitals and natural transition orbitals, linking theoretical quantum mechanics to observable molecular properties through spectroscopic data. These orbitals provide a bridge between abstract models and experimental reality in chemistry.

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Last Updated: Dec 10, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs

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Area of Science:

Quantum chemistry
Spectroscopy
Molecular physics

Background:

Molecular orbital theory is crucial for understanding molecular properties.
Hartree-Fock and Kohn-Sham orbitals are approximations and not directly observable.
Quantum mechanics provides a theoretical link between wavefunctions and observable properties.

Purpose of the Study:

To discuss Dyson orbitals and natural transition orbitals.
To illustrate their application in modeling and interpreting spectroscopic measurements.
To connect theoretical orbital concepts with experimental data.

Main Methods:

Theoretical analysis of quantum mechanical principles.
Discussion of Dyson orbitals and natural transition orbitals.
Application in the context of spectroscopic data interpretation.

Main Results:

Dyson orbitals and natural transition orbitals can be reconstructed from experimental data.
These orbitals offer a way to interpret spectroscopic measurements.
Provides a framework for linking theoretical models to observable phenomena.

Conclusions:

Dyson orbitals and natural transition orbitals are valuable tools for interpreting spectroscopic data.
These orbitals bridge the gap between theoretical constructs and experimental observations.
Enhances the understanding of molecular properties through observable measurements.