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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

Molecular Orbital Theory II

Molecular Orbital Theory II

Molecular Orbital Energy Diagrams

Hybridization of Atomic Orbitals II

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

Hybridization of Atomic Orbitals I

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...

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: Feb 12, 2026

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

Published on: December 15, 2021

Solitonic natural orbitals.

Jerzy Cioslowski¹

¹Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland and Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden, Germany.

The Journal of Chemical Physics

|April 9, 2018

Summary

This summary is machine-generated.

The harmonium atom

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Area of Science:

Quantum chemistry
Atomic physics
Computational physics

Background:

The behavior of electrons in confined atomic systems is crucial for understanding chemical bonding and material properties.
The harmonium atom model provides a simplified yet insightful system for studying electron correlation under confinement.

Purpose of the Study:

To investigate the dependence of natural amplitudes of the harmonium atom's ground state on confinement strength (ω).
To identify the emergence and characteristics of unusual natural orbitals (NOs) and their associated natural amplitudes under varying confinement conditions.

Main Methods:

Rigorous analytical methods.
Highly accurate numerical calculations.
Analysis of natural orbitals and natural amplitudes.

Main Results:

A single positive-valued natural amplitude (normal sign pattern) is observed for all confinement strengths ω ≥ 12.
Weakening confinement below critical values leads to the emergence of unusual, weakly occupied natural orbitals (NOs).
These solitonic NOs exhibit radial localization and near-invariant shapes as they approach infinite radial positions.

Conclusions:

The study reveals a transition in the natural amplitude behavior of the harmonium atom as confinement weakens.
Emergent solitonic NOs offer insights into electron behavior in weakly confined and potentially Coulombic systems.
The findings have implications for understanding electron correlation in various atomic and molecular systems.