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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.

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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Molecular Orbital Theory I

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Molecular Orbital Theory II

Molecular Orbital Theory II

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Reduced Mass Coordinates: Isolated Two-body Problem

Reduced Mass Coordinates: Isolated Two-body Problem

In classical mechanics, the two-body problem is one of the fundamental problems describing the motion of two interacting bodies under gravity or any other central force. When considering the motion of two bodies, one of the most important concepts is the reduced mass coordinates, a quantity that allows the two-body problem to be solved like a single-body problem. In these circumstances, it is assumed that a single body with reduced mass revolves around another body fixed in a position with an...

MO Theory and Covalent Bonding

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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...

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Related Experiment Video

Updated: Jul 7, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Local-density approximation for orbital densities applied to the self-interaction correction.

Naoto Umezawa¹

¹National Institute for Materials Science, Advanced Electronic Materials Center, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan. umezawa.naoto@nims.go.jp

The Journal of Chemical Physics

|February 6, 2008

Summary

A new approximation simplifies self-interaction correction in density functional theory. This method accurately estimates atomic energies, ionization potentials, and electron affinities, offering a practical computational tool.

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Last Updated: Jul 7, 2026

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Published on: May 27, 2020

Area of Science:

Quantum Chemistry
Computational Physics
Materials Science

Background:

Self-interaction error is a known issue in local spin density functional approximations.
Accurate calculations of atomic properties are crucial for understanding chemical behavior.

Purpose of the Study:

To propose a simple and effective approximation for the functional derivative in Perdew-Zunger-type self-interaction-corrected local-spin density functionals.
To evaluate the performance of this new approximation for atomic properties.

Main Methods:

Approximating orbital density as a functional of local electron density.
Calculating functional derivatives based on this approximation.
Performing computational studies on atomic properties.

Main Results:

The proposed approximation provides good estimates for total energy, ionization potential, and electron affinity in atoms.
Comparative analysis shows competitive performance against existing methods like averaged-density approximation and global averaging.

Conclusions:

The suggested approximation offers a computationally efficient and accurate method for self-interaction correction.
This approach holds promise for improving the predictive power of density functional theory in atomic and molecular calculations.