Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Atomic Orbitals02:44

Atomic Orbitals

47.3K
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.
47.3K
The Energies of Atomic Orbitals03:21

The Energies of Atomic Orbitals

31.1K
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.
31.1K
Molecular Orbital Theory I02:35

Molecular Orbital Theory I

49.2K
Overview of Molecular Orbital Theory
49.2K
Hybridization of Atomic Orbitals I03:24

Hybridization of Atomic Orbitals I

69.3K
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...
69.3K
The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

61.4K
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
61.4K
Molecular Orbital Theory II03:51

Molecular Orbital Theory II

28.4K
Molecular Orbital Energy Diagrams
28.4K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Universal Exchange-Correlation Surface Asymptotics: Metal Slabs Versus Semi-infinite Metal Surfaces.

Physical review letters·2025
Same author

Orbital-free density-functional theory for metal slabs.

The Journal of chemical physics·2023
Same author

From Alpha Diversity to Zzz: Interactions among sleep, the brain, and gut microbiota in the first year of life.

Progress in neurobiology·2021
Same author

Approximate expression for the ground-state energy of the two- and three-dimensional Hubbard model at arbitrary filling obtained from dimensional scaling.

Journal of physics. Condensed matter : an Institute of Physics journal·2019
Same author

Transport through correlated systems with density functional theory.

Journal of physics. Condensed matter : an Institute of Physics journal·2017
Same author

Investigation of Self-Interaction Corrections for an Exactly Solvable Model System: Orbital Dependence and Electron Localization.

Journal of chemical theory and computation·2015

Related Experiment Video

Updated: Mar 29, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

8.8K

Dependence of Response Functions and Orbital Functionals on Occupation Numbers.

S Kurth1, C R Proetto1, K Capelle1

  • 1Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany.

Journal of Chemical Theory and Computation
|November 27, 2015
PubMed
Summary

Density functional theory calculations often depend on Kohn-Sham orbitals and occupation numbers. This study clarifies when variations in occupation numbers are justified in optimized effective potential calculations for accurate exchange-correlation potentials.

More Related Videos

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

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

Published on: May 27, 2020

9.1K
Thermochemical Studies of NiII and ZnII Ternary Complexes Using Ion Mobility-Mass Spectrometry
16:11

Thermochemical Studies of NiII and ZnII Ternary Complexes Using Ion Mobility-Mass Spectrometry

Published on: June 8, 2022

2.8K

Related Experiment Videos

Last Updated: Mar 29, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

8.8K
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

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

Published on: May 27, 2020

9.1K
Thermochemical Studies of NiII and ZnII Ternary Complexes Using Ion Mobility-Mass Spectrometry
16:11

Thermochemical Studies of NiII and ZnII Ternary Complexes Using Ion Mobility-Mass Spectrometry

Published on: June 8, 2022

2.8K

Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Materials Science

Background:

  • Density functional theory (DFT) is a powerful quantum mechanical modeling method.
  • Exchange-correlation functionals are key to DFT accuracy.
  • Orbital-dependent functionals require accurate Kohn-Sham orbitals and occupation numbers.

Purpose of the Study:

  • To investigate the validity of approximations in calculating exchange-correlation potentials.
  • To determine conditions under which occupation number variations are justified in optimized effective potential (OEP) methods.
  • To improve the accuracy of DFT calculations using orbital-dependent functionals.

Main Methods:

  • Analysis of explicitly orbital-dependent exchange-correlation energy functionals.
  • Application of the optimized effective potential (OEP) method.
  • Examination of the variation of occupation numbers with respect to the effective single-particle potential.

Main Results:

  • Identified specific circumstances where the standard OEP procedure is justified.
  • Demonstrated the importance of considering occupation number variations for certain functionals.
  • Provided criteria for the appropriate application of OEP methods.

Conclusions:

  • The treatment of occupation number variations in OEP calculations is crucial for accuracy.
  • The study offers a theoretical basis for simplifying OEP calculations under certain conditions.
  • Findings contribute to the development of more reliable DFT methods for electronic structure calculations.